Sam Clearman ; Matthew Hyatt ; Brittany Shelton ; Mark Skandera
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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)
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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 1; Mark Skandera 1
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Sam Clearman;Matthew Hyatt;Brittany Shelton;Mark Skandera
1 Department of Mathematics
For irreducible characters {χλq|λ⊢n} and induced sign characters {ϵλq|λ⊢n} of the Hecke algebra Hn(q), and Kazhdan-Lusztig basis elements C′w(q) with w avoiding the pattern 312, we combinatorially interpret the polynomials χλq(qℓ(w)2C′w(q)) and ϵλq(qℓ(w)2C′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 Hn(q)-traces.
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