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 elementsArticle
Authors: Sam Clearman 1; Matthew Hyatt 1; Brittany Shelton 1; Mark Skandera 1
NULL##NULL##0000-0002-3751-5660##NULL
Sam Clearman;Matthew Hyatt;Brittany Shelton;Mark Skandera
1 Department of Mathematics
For irreducible characters $\{ \chi_q^{\lambda} | \lambda \vdash n\}$ and induced sign characters $\{\epsilon_q^{\lambda} | \lambda \vdash n\}$ of the Hecke algebra $H_n(q)$, and Kazhdan-Lusztig basis elements $C'_w(q)$ with $w$ avoiding the pattern 312, we combinatorially interpret the polynomials $\chi_q^{\lambda}(q^{\frac{\ell(w)}{2}} C'_w(q))$ and $\epsilon_q^{\lambda}(q^{\frac{\ell(w)}{2}} C'_w(q))$. 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 $H_n(q)$-traces.
Byung-Hak Hwang, 2023, Chromatic quasisymmetric functions and noncommutative 𝑃-symmetric functions, Transactions of the American Mathematical Society, 10.1090/tran/9096.
Soojin Cho;JiSun Huh, 2019, On $e$-Positivity and $e$-Unimodality of Chromatic Quasi-symmetric Functions, arXiv (Cornell University), 33, 4, pp. 2286-2315, 10.1137/18m1216201, http://arxiv.org/abs/1711.07152.
Ryan Kaliszewski;Justin Lambright;Mark Skandera, 2018, Bases of the quantum matrix bialgebra and induced sign characters of the Hecke algebra, Journal of Algebraic Combinatorics, 49, 4, pp. 475-505, 10.1007/s10801-018-0832-4, https://doi.org/10.1007/s10801-018-0832-4.