Combinatorial Gelfand Models

Ron M. Adin; Alex Postnikov; Yuval Roichman

doi:10.46298/dmtcs.3612

Ron M. Adin ; Alex Postnikov ; Yuval Roichman - Combinatorial Gelfand Models

dmtcs:3612 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3612

Combinatorial Gelfand ModelsConference paper

Authors: Ron M. Adin ¹; Alex Postnikov ²; Yuval Roichman ¹

1 Department of Mathematics [Bar-Ilan]
2 Department of Applied Mathematics

A combinatorial construction of Gelfand models for the symmetric group, for its Iwahori-Hecke algebra and for the hyperoctahedral group is presented.

https://doi.org/10.46298/dmtcs.3612

Source: HAL:hal-01185146v1

Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)

Section: Proceedings

Published on: January 1, 2008

Imported on: May 10, 2017

Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] symmetric group, hyperoctahedral group, Iwahori-Hecke algebra, descents, inversions, character formulas, Gelfand model

Bibliographic References

25 Documents citing this article

Avichai Marmor, 2024, Schur-positivity of short chords in matchings, Algebraic Combinatorics, 7, 3, pp. 887-914, 10.5802/alco.351, https://doi.org/10.5802/alco.351.

Eric Marberg;Yifeng Zhang, 2024, Insertion Algorithms for Gelfand $$S_n$$-Graphs, Annals of Combinatorics, 28, 4, pp. 1199-1242, 10.1007/s00026-024-00701-6, https://doi.org/10.1007/s00026-024-00701-6.

Sherry H.F. Yan;Zonglin Yang;Robin D.P. Zhou, 2024, On Schur-positivity of the descent set on matchings, Discrete Mathematics, 347, 7, pp. 114017, 10.1016/j.disc.2024.114017.

Eric Marberg;Yifeng Zhang, 2022, Gelfand W-graphs for classical Weyl groups, arXiv (Cornell University), 609, pp. 292-336, 10.1016/j.jalgebra.2022.06.023, http://arxiv.org/abs/2012.13868.

Eric Marberg;Yifeng Zhang, 2022, Perfect models for finite Coxeter groups, Journal of Pure and Applied Algebra, 227, 5, pp. 107303, 10.1016/j.jpaa.2022.107303.

Kassie Archer;Virginia Germany;C. Marin King;L.-K. Lauderdale, 2022, Involutions and the Gelfand character, Journal of Algebraic Combinatorics, 57, 3, pp. 811-828, 10.1007/s10801-022-01194-3.

Georgia Benkart;Tom Halverson;Nate Harman, 2017, Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups, arXiv (Cornell University), 46, 1, pp. 77-108, 10.1007/s10801-017-0748-4, http://arxiv.org/abs/1605.06543.

Ron M. Adin;Christos A. Athanasiadis;Sergi Elizalde;Yuval Roichman, 2017, Character formulas and descents for the hyperoctahedral group, arXiv (Cornell University), 87, pp. 128-169, 10.1016/j.aam.2017.01.004, http://arxiv.org/abs/1504.01283.

Yacine Barhoumi-Andréani, 2017, Random Characters under the $L$-Measure, I: Dirichlet Characters, arXiv (Cornell University), 2019, 7, pp. 1974-2007, 10.1093/imrn/rnx168, http://arxiv.org/abs/1701.04258.

Kassie Archer, 2016, Descents of λ-unimodal cycles in a character formula, Discrete Mathematics, 339, 10, pp. 2399-2409, 10.1016/j.disc.2016.04.006.

Eric Marberg;Eric Marberg, 2015, Strong forms of self-duality for Hopf monoids in species, arXiv (Cornell University), 368, 8, pp. 5433-5473, 10.1090/tran/6506, http://arxiv.org/abs/1312.4681.

Fabrizio Caselli;Eric Marberg, 2015, Generalized Involution Models of Projective Reflection Groups, Springer INdAM series, pp. 19-23, 10.1007/978-3-319-20155-9_5.

Volodymyr Mazorchuk;Catharina Stroppel, 2015, $$G(\ell ,k,d)$$ G ( ℓ , k , d ) -modules via groupoids, MPG.PuRe (Max Planck Society), 43, 1, pp. 11-32, 10.1007/s10801-015-0623-0, http://hdl.handle.net/21.11116/0000-0004-101D-A.

José O. Araujo;Tim Bratten, 2014, Gelfand models for classical Weyl groups, arXiv (Cornell University), 403, pp. 154-178, 10.1016/j.jalgebra.2014.01.009, http://arxiv.org/abs/1112.3585.

Ron M. Adin;Yuval Roichman, 2014, Matrices, characters and descents, arXiv (Cornell University), 469, pp. 381-418, 10.1016/j.laa.2014.11.028, http://arxiv.org/abs/1301.1675.

Tom Halverson;Mike Reeks, 2014, Gelfand models for diagram algebras, Journal of Algebraic Combinatorics, 41, 2, pp. 229-255, 10.1007/s10801-014-0534-5, https://doi.org/10.1007/s10801-014-0534-5.

Eric Marberg, 2013, How to compute the Frobenius–Schur indicator of a unipotent character of a finite Coxeter system, arXiv (Cornell University), 240, pp. 484-519, 10.1016/j.aim.2013.02.023, http://arxiv.org/abs/1202.1311.

Fabrizio Caselli;Eric Marberg, 2013, Isomorphisms, automorphisms, and generalized involution models of projective reflection groups, arXiv (Cornell University), 199, 1, pp. 433-483, 10.1007/s11856-013-0044-5, http://arxiv.org/abs/1208.6336.

Sergi Elizalde;Yuval Roichman, 2013, Arc permutations, Journal of Algebraic Combinatorics, 39, 2, pp. 301-334, 10.1007/s10801-013-0449-6, https://doi.org/10.1007/s10801-013-0449-6.

Volodymyr Mazorchuk, 2013, Combinatorial Gelfand Models for Semisimple Diagram Algebras, Milan Journal of Mathematics, 81, 2, pp. 385-396, 10.1007/s00032-013-0206-2.

Eric Marberg;Eric Marberg, 2012, Generalized involution models for wreath products, arXiv (Cornell University), 192, 1, pp. 157-195, 10.1007/s11856-012-0021-4, http://arxiv.org/abs/1007.5078.

Eric Marberg, 2011, Automorphisms and generalized involution models of finite complex reflection groups, arXiv (Cornell University), 334, 1, pp. 295-320, 10.1016/j.jalgebra.2011.02.021, http://arxiv.org/abs/1007.4886.

Pierre-Loïc Méliot, 2011, Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract), Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings vol. AO,..., Proceedings, 10.46298/dmtcs.2943, https://doi.org/10.46298/dmtcs.2943.

A. Berenstein;J. Greenstein, 2010, Quantum Folding, arXiv (Cornell University), 10.1093/imrn/rnq264, http://arxiv.org/abs/1007.4357.

Fabrizio Caselli, 2010, Involutory reflection groups and their models, Journal of Algebra, 324, 3, pp. 370-393, 10.1016/j.jalgebra.2010.04.017.

Sources : OpenCitations, OpenAlex & Crossref

Share and export

Consultation statistics

This page has been seen 405 times.

This article's PDF has been downloaded 398 times.