Universität Bonn

Trimester Program: "On the Interaction of Representation Theory with Geometry and Combinatorics"

January - April 2011

Organizers: Steffen König, Peter Littelmann, Jan Schröer, Catharina Stroppel

Description: Representation theory is one of the most vibrant fields of mathematics today. Starting with the pioneering work of Frobenius, Burnside and Schur, its history is a story rich in innovation and implementation of techniques from throughout mathematics. By its very nature, representation theory lies at the intersection of several fields: algebra, Lie theory, algebraic geometry, topology, number theory, differential geometry, combinatorics, harmonic analysis and mathematical physics.

The Hausdorff Trimester Program provided a forum and meeting place for exchange of ideas and techniques, focussing on topics connecting representation theory with different areas of mathematics. It brought together leading experts from representation theory, geometry, and combinatorics and, at the same time, enhanced the exchange between the various research networks.

The focus was on the following research topics:

  • Geometrization, categorification and integral canonical structures
  • Homological aspects of representation theory
  • Representations of Cherednik algebras
  • (Finite dimensional) algebras and cluster algebras
  • Infinite-dimensional Lie algebras and related algebraic structures
  • Combinatorics of flag varieties and Schubert calculus
  • Hecke algebras, Koszul duality and tilting theory

Associated Events: Workshop, Winter School

Publications

No. Author(s) Title Preprint Publication
2011a01 Cerulli Irelli, G. Positivity in skew-symmetric cluster algebras of finite type 1102.30504  
2011a02 Chari, V.; Loktev, S. An application of global Weyl modules of sln+1[t] to invariant theory 1104.40485 J. Algebra. 349 (2012), 317–328.
https://doi.org/10.1016/j.jalgebra.2011.09.0176
2011a03 Feigin, E.; Finkelberg, M. Degenerate flag varieties of type A: Frobenius splitting and BW theorem 1103.14917 Math. Z. 275(1-2) (2013), 55–77.
https://doi.org/10.1007/s00209-012-1122-98
2011a04 Fourier, G.; Khandai, T.; Kus, D.; Savage, A. Local Weyl modules for equivariant map algebras with free abelian group actions 1103.57669 J. Algebra. 350 (2012), 386–404.
https://doi.org/10.1016/j.jalgebra.2011.10.01810
2011a05 Gaussent, S.; Littelmann, P. One-skeleton galleries, the path model, and a generalization of Macdonald's formula for Hall-Littlewood polynomials 1004.006611 Int. Math. Res. Not. IMRN 2012(12) (2012), 2649–2707.
https://doi.org/10.1093/imrn/rnr10812
2011a06 Kleshchev, A. S.; Mathas, A.; Ram, A. Universal graded Specht modules for cyclotomic Hecke algebras 1102.351913 Proc. Lond. Math. Soc. 105(6) (2012), 1245–1289.
https://doi.org/10.1112/plms/pds01914
2011a07 Lanini, M. Kazhdan-Lusztig combinatorics in the moment graph setting 1103.228215 J. Algebra. 370 (2012), 152–170.
https://doi.org/10.1016/j.jalgebra.2012.07.02316
2011a08 Neher, E.; Savage, A. Extensions and block decompositions for finite-dimensional representations of equivariant map algebras 1103.436717 Transform. Groups. 20(1) (2015), 183–228.
https://doi.org/10.1007/s00031-015-9300-618
2011a09 Reineke, M. Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for m-loop quivers 1102.397819 Doc. Math. 17 (2012), 1–22.
https://doi.org/10.4171/dm/35920
2011a10 Reineke, M.; Weist, T. Refined GW/Kronecker correspondence 1103.528321 Math. Ann. 355(1) (2013), 17–56.
https://doi.org/10.1007/s00208-012-0778-022
2011a11 Ringel, C. M. Cluster-additive functions on stable translation quivers 1105.152923 J. Algebraic Combin. 36(3) (2012), 475–500.
https://doi.org/10.1007/s10801-012-0346-424
2011a12 Schilling, A.; Tingley, P. Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function 1104.235925 Electron. J. Combin.19(2) (2012).
https://doi.org/10.37236/218426
2011a13 Achar, P. N.; Stroppel, C. Completions of Grothendieck groups 1105.271527 Bull. Lond. Math. Soc. 45(1) (2013), 200–212.
https://doi.org/10.1112/blms/bds07928
2011a14 Angeleri Hügel, L.; Koenig, S.; Liu, Q.; Yang, D. Stratifying derived module categories C. R. Math. Acad. Sci. Paris. 349(21-22) (2011), 1139–1144.
https://doi.org/10.1016/j.crma.2011.06.01829
2011a15 Angeleri Hügel, L.; Koenig, S.; Liu, Q. Jordan-Hölder theorems for derived module categories of piecewise hereditary algebras 1104.341830 J. Algebra. 352 (2012), 361–381.
https://doi.org/10.1016/j.jalgebra.2011.09.04131
2011a16 Brundan, J.; Stroppel, C. Gradings on walled Brauer algebras and Khovanov's arc algebra 1107.099932 Adv. Math. 231(2) (2012), 709–773.
https://doi.org/10.1016/j.aim.2012.05.01633
2011a17 Cerulli Irelli, G.; Feigin, E.; Reineke, M. Quiver Grassmannians and degenerate flag varieties 1106.239934 Algebra Number Theory. 6(1) (2012), 165–194.
https://doi.org/10.2140/ant.2012.6.16535
2011a18 Feigin, E.; Finkelberg, M.; Littelmann, P. Symplectic degenerate flag varieties 1106.139936 Canad. J. Math. 66(6) (2014), 1250–1286.
https://doi.org/10.4153/CJM-2013-038-637
2011a19 Hiss, G.; König, S.; Naehrig, N. On the socle of an endomorphism algebra pdf38 J. Pure Appl. Algebra. 216(6) (2012), 1288–1294.
https://doi.org/10.1016/j.jpaa.2011.12.01439
2011a20 Iyengar, S. B.; Krause, H. The Bousfield lattice of a triangulated category and stratification 1105.179940 Math. Z. 273(3-4) (2013), 1215–1241.
https://doi.org/10.1007/s00209-012-1051-741
2011a21 Kang, S-J.; Kashiwara, M.; Tsuchioka, S. Quiver Hecke superalgebras 1107.103942 J. Reine Angew. Math.711 (2016), 1–54.
https://doi.org/10.1515/crelle-2013-008943
2011a22 Liu, Q.; Yang, D. Blocks of group algebras are derived simple 1104.050044 Math. Z. 272(3-4) (2012), 913–920.
https://doi.org/10.1007/s00209-011-0963-y45
2011a23 Neeb, K-H. Semibounded representations of Hermitian Lie groups 1104.223446 Trav. Math. 21 (2012), 29-109.
https://cris.fau.de/publications/116127044/47
2011a24 Cerulli Irelli, G.; Labardini-Fragoso, D. Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials 1108.177448 Compos. Math. 148(6) (2012), 1833–1866.
https://doi.org/10.1112/S0010437X1200052849
2011a25 De Concini, C.; Maffei, A. A generalized Steinberg section and branching rules for quantum groups at roots of 1 1107.024850 Mosc. Math. J. 12(3) (2012), 469–495.
https://doi.org/10.17323/1609-4514-2012-12-3-469-49551
2011a26 Geiss, C.; Leclerc, B.; Schröer, J. Cluster structures on quantum coordinate rings 1104.053152 Selecta Math. (N.S.) 19(2) (2013), 337–397.
https://doi.org/10.1007/s00029-012-0099-x53
2011a27 Speyer, D.; Thomas, H. Acyclic cluster algebras revisited 1203.027754 Algebras, quivers and representations. (2013), 275–298.
https://doi.org/10.1007/978-3-642-39485-0_1255
2011a28 Dupont, G.; Thomas, H. Atomic bases in cluster algebras of types A and à 1106.375856 Proc. Lond. Math. Soc. 107(4) (2013), 825–850.
https://doi.org/10.1112/plms/pdt00157
2011a29 Chen, H.; Xi, C. Stratifications of derived categories from tilting modules over tame hereditary algebras 1107.044458  
2011a30 Fourier, G.; Manning, N.; Senesi, P. Global Weyl modules for the twisted loop algebra 1110.275259 Abh. Math. Semin. Univ. Hambg. 83(1) (2013), 53–82.
https://doi.org/10.1007/s12188-013-0074-260
2011a31 Hilgert, J.; Kobayashi, T.; Möllers, J. Minimal representations via Bessel operators 1106.362161 J. Math. Soc. Japan. 66(2) (2014), 349–414.
https://doi.org/10.2969/jmsj/0662034962
2011a32 Brion, M. Invariant Hilbert schemes 1102.019863
2011a33 Brion, M. Homogeneous bundles over abelian varieties 1101.277164 J. Ramanujan Math. Soc. 27(1) (2012), 91–118.
https://jrms.ramanujanmathsociety.org/archieves/v27-1.html65
2011a34 Brion, M. Homogeneous projective bundles over abelian varieties 1104.081866 Algebra Number Theory. 7(10) (2013), 2475–2510.
https://doi.org/10.2140/ant.2013.7.247567
2011a35 Lenart, C.; Schilling, A. Crystal energy functions via the charge in types A and C 1107.416968 Math. Z. 273(1-2) (2013), 401–426.
https://doi.org/10.1007/s00209-012-1011-269
2011a36 Bump, D.; Salisbury, B.; Schilling, A. Lie methods and related combinatorics in Sage link70  
2011a37 Brav, C.; Thomas, H. Thin monodromy in Sp(4) 1210.052371 Compos. Math. 150(3) (2014), 333–343.
https://doi.org/10.1112/S0010437X1300755072
2011a38 Chari, V.; Fourier, G.; Sagaki, D. Posets, tensor products and Schur positivity 1210.618473 Algebra Number Theory. 8(4) (2014), 933–961.
https://doi.org/10.2140/ant.2014.8.93374
2011a39 Bennett, M.; Chari, V.; Manning, N. BGG reciprocity for current algebras 1106.034775 Adv. Math. 231(1) (2012), 276–305.
https://doi.org/10.1016/j.aim.2012.05.00576
2011a40 Chlouveraki, M.; Gordon, I.; Griffeth, S. Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras 1104.407077 New trends in noncommutative algebra. (2012), 77–89.
https://doi.org/10.1090/conm/562/1113178
2011a41 Geiss, C.; Leclerc, B.; Schröer, J. Factorial cluster algebras 1110.119979 Doc. Math. 18 (2013), 249–274.
https://doi.org/10.4171/dm/39680
2011a42 Wenzl, H. On centralizer algebras for spin representations 1107.418381 Comm. Math. Phys. 314(1) (2012), 243–263.
https://doi.org/10.1007/s00220-012-1494-z82
2011a43 Fomin, S.; Pylyavskyy, P. Tensor diagrams and cluster algebras 1210.188883 Adv. Math. 300 (2016), 717–787.
https://doi.org/10.1016/j.aim.2016.03.03084
2011a44 Gordon, I. G.; Losev, I. On category O for cyclotomic rational Cherednik algebras 1109.231585 J. Eur. Math. Soc. (JEMS) 16(5) (2014), 1017–1079.
https://doi.org/10.4171/JEMS/45486

Participants

Name
Affiliation
Lidia Angeleri Hügel Università di Verona
Susumu Ariki Osaka University
Arkady Berenstein University of Oregon
Michel Brion Université Grenoble
Jonathan Brundan University of Oregon
Vyjayanthi Chari University of California at Riverside
Joseph Chuang City University London
Corrado De Concini Università "La Sapienza" Roma
Stéphanie Cupit-Foutou Universität Köln
Felix Dietlein Universität Köln
Michael Ehrig Universität Bonn
Ming Fang Chinese Academy of Science
Evgeny Feigin University - Higher School of Economics HSE
Peter Fiebig Universität Erlangen-Nürnberg
Sergey Fomin University of Michigan
Ghislain Fourier Universität Köln
Stéphane Gaussent Université Henri Poincaré Nancy I
Iain Gordon University of Edinburgh
Qiong Guo Universität Stuttgart
Henning Haahr-Andersen Aarhus University
Anne Henke Oxford University
Joachim Hilgert Universität Paderborn
Joachim Hilgert Universität Paderborn
Gerhard Hiß RWTH Aachen
Giovanni Cerulli Irelli Università "La Sapienza" Roma
Rollo Crozier John Jenkins University of Edinburgh
Yong Jiang Universität Bielefeld
Masaki Kashiwara Kyoto University
Alexander Kleshchev University of Oregon
Inka Klostermann Universität Köln
Toshiyuki Kobayashi University of Tokyo
Stavros Kousidis Universität Köln
Henning Krause Universität Bielefeld
Shrawan Kumar University of North Carolina at Chapel Hill
Shrawan Kumar University of North Carolina at Chapel Hill
Deniz Kus Universität Köln
Steffen König Universität Stuttgart
Martina Lanini Universita' degli Studi di Roma Tre
Bernard Leclerc LMNO Université de Caen
Brandyn Lee The University of North Carolina at Chapel Hill
Émilie Liboz Université de Besançon
Peter Littelmann Universität Köln
Dong Liu Universität Köln
Qunhua Liu Universität Stuttgart
Sergey Loktev Higher School of Economics
Ivan Loseu Massachusetts Institute of Technology/MIT
Andrea Maffei Università di Roma "La Sapienza"
Gunter Malle TU Kaiserslautern
Nathaniael Manning University of California, Riverside
Maurizio Martino Universität Bonn
Vanessa Miemietz University of East Anglia
Luca Moci TU Berlin
Hiraku Nakajima Kyoto University
Karl-Hermann Neeb FAU Erlangen-Nürnberg
An Hoa Nguyen Universität Köln
Bruno Niemann Universität Köln
Eric M. Opdam Universität Amsterdam
Santosha Kumar Pattanayak Chennai Mathematical Institute
Thomas Quella University of Cologne
Arun Ram University of Melbourne
Markus Reineke Bergische Universität Wuppertal
Idun Reiten NTNU Norges teknisk-naturvitenskapelige universitet
Claus Michael Ringel Universität Bielefeld
Adam-Christiaan Ruben van Roosmalen MPI Bonn
Amber Russell Louisiana State University
Steen Ryom-Hansen Universidad de Talca
Daisuke Sagaki University of Tsukuba
Selene Sanchez-Flores Universität Stuttgart
Alistair Savage University of Ottawa
Ralf Schiffler University of Connecticut
Olivier Schiffmann Université Paris-Sud 11
Anne Schilling University of California at Davis
Olaf Schnürer Universität Bonn
Jan Schröer Universität Bonn
Bea Schumann Universität Köln
Armin Shalile Universität Stuttgart
Christopher Spencer University of Edinburgh
John Tobias Stafford Mancester University
Friederike Stoll Universität Stuttgart
Catharina Stroppel Universität Bonn
Harry Tamvakis University of Maryland
Hugh Thomas University of New Brunswick
Jorge Vitória Universität Stuttgart
Hans Wenzl University of California San Diego
Changchang Xi Beijing Normal University
Oksana Yakimova Universität Köln
Dong Yang Max-Planck Institut für Mathematik Bonn
Andrei Zelevinsky Northeastern University

This list does not include people who only participated in the workshop or the winter school.

Poster TP_2011_01.jpg
© HIM

Links

  1. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2011_01#pubs
  2. https://www.mathematics.uni-bonn.de/en/programs/assets/report-tp_2011_01.pdf
  3. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2011_01#part
  4. http://arxiv.org/abs/1102.3050
  5. http://arxiv.org/abs/1104.4048
  6. https://doi.org/10.1016/j.jalgebra.2011.09.017
  7. http://arxiv.org/abs/1103.1491
  8. https://doi.org/10.1007/s00209-012-1122-9
  9. http://arxiv.org/abs/1103.5766
  10. https://doi.org/10.1016/j.jalgebra.2011.10.018
  11. http://arxiv.org/abs/1004.0066
  12. https://doi.org/10.1093/imrn/rnr108
  13. http://arxiv.org/abs/1102.3519
  14. https://doi.org/10.1112/plms/pds019
  15. http://arxiv.org/abs/1103.2282
  16. https://doi.org/10.1016/j.jalgebra.2012.07.023
  17. http://arxiv.org/abs/1103.4367
  18. https://doi.org/10.1007/s00031-015-9300-6
  19. http://arxiv.org/abs/1102.3978
  20. https://doi.org/10.4171/dm/359
  21. http://arxiv.org/abs/1103.5283
  22. https://doi.org/10.1007/s00208-012-0778-0
  23. http://arxiv.org/abs/1105.1529
  24. https://doi.org/10.1007/s10801-012-0346-4
  25. http://arxiv.org/abs/1104.2359
  26. https://doi.org/10.37236/2184
  27. http://arxiv.org/abs/1105.2715
  28. https://doi.org/10.1112/blms/bds079
  29. https://doi.org/10.1016/j.crma.2011.06.018
  30. http://arxiv.org/abs/1104.3418
  31. https://doi.org/10.1016/j.jalgebra.2011.09.041
  32. http://arxiv.org/abs/1107.0999
  33. https://doi.org/10.1016/j.aim.2012.05.016
  34. http://arxiv.org/abs/1106.2399
  35. https://doi.org/10.2140/ant.2012.6.165
  36. http://arxiv.org/abs/1106.1399
  37. https://doi.org/10.4153/CJM-2013-038-6
  38. https://www.mathematics.uni-bonn.de/en/programs/assets/2011a19.pdf
  39. https://doi.org/10.1016/j.jpaa.2011.12.014
  40. http://arxiv.org/abs/1105.1799
  41. https://doi.org/10.1007/s00209-012-1051-7
  42. http://arxiv.org/abs/1107.1039
  43. https://doi.org/10.1515/crelle-2013-0089
  44. http://arxiv.org/abs/1104.0500
  45. https://doi.org/10.1007/s00209-011-0963-y
  46. http://arxiv.org/abs/1104.2234
  47. https://cris.fau.de/publications/116127044/
  48. http://arxiv.org/abs/1108.1774
  49. https://doi.org/10.1112/S0010437X12000528
  50. http://arxiv.org/abs/1107.0248
  51. https://doi.org/10.17323/1609-4514-2012-12-3-469-495
  52. http://arxiv.org/abs/1104.0531
  53. https://doi.org/10.1007/s00029-012-0099-x
  54. http://arxiv.org/abs/1203.0277
  55. https://doi.org/10.1007/978-3-642-39485-0_12
  56. http://arxiv.org/abs/1106.3758
  57. https://doi.org/10.1112/plms/pdt001
  58. http://arxiv.org/abs/1107.0444
  59. http://arxiv.org/abs/1110.2752
  60. https://doi.org/10.1007/s12188-013-0074-2
  61. http://arxiv.org/abs/1106.3621
  62. https://doi.org/10.2969/jmsj/06620349
  63. http://arxiv.org/abs/1102.0198
  64. http://arxiv.org/abs/1101.2771
  65. https://jrms.ramanujanmathsociety.org/archieves/v27-1.html
  66. http://arxiv.org/abs/1104.0818
  67. https://doi.org/10.2140/ant.2013.7.2475
  68. http://arxiv.org/abs/1107.4169
  69. https://doi.org/10.1007/s00209-012-1011-2
  70. http://doc.sagemath.org/html/en/thematic_tutorials/lie.html
  71. http://arxiv.org/abs/1210.0523
  72. https://doi.org/10.1112/S0010437X13007550
  73. http://arxiv.org/abs/1210.6184
  74. https://doi.org/10.2140/ant.2014.8.933
  75. http://arxiv.org/abs/1106.0347
  76. https://doi.org/10.1016/j.aim.2012.05.005
  77. http://arxiv.org/abs/1104.4070
  78. https://doi.org/10.1090/conm/562/11131
  79. http://arxiv.org/abs/1110.1199
  80. https://doi.org/10.4171/dm/396
  81. http://arxiv.org/abs/1107.4183
  82. https://doi.org/10.1007/s00220-012-1494-z
  83. http://arxiv.org/abs/1210.1888
  84. https://doi.org/10.1016/j.aim.2016.03.030
  85. http://arxiv.org/abs/1109.2315
  86. https://doi.org/10.4171/JEMS/454
  87. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2011_01#start