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 ORCID1; Mark Skandera 1

  • 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.


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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