Sam Clearman ; Matthew Hyatt ; Brittany Shelton ; Mark Skandera - Evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements

dmtcs:2368 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2368
Evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elementsConference paper

Authors: Sam Clearman 1; Matthew Hyatt 1; Brittany Shelton ORCID1; Mark Skandera 1

  • 1 Department of Mathematics

For irreducible characters {χλq|λn} and induced sign characters {ϵλq|λn} of the Hecke algebra Hn(q), and Kazhdan-Lusztig basis elements Cw(q) with w avoiding the pattern 312, we combinatorially interpret the polynomials χλq(q(w)2Cw(q)) and ϵλq(q(w)2Cw(q)). This gives a new algebraic interpretation of q-chromatic symmetric functions of Shareshian and Wachs. We conjecture similar interpretations and generating functions corresponding to other Hn(q)-traces.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Hecke algebra,trace,Kazhdan-Lusztig basis,tableau,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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