LLT Polynomials and Hecke Algebra Traces
Alejandro H. Morales (Universit\'e du Qu\'ebec \`a Montr\'eal), Mark, A. Skandera (Lehigh University), Jiayuan Wang (Lehigh University)
TL;DR
This paper establishes a connection between unicellular LLT polynomial coefficients and Hecke algebra traces, providing new formulas involving Kazhdan-Lusztig bases and R-polynomials.
Contribution
It reveals that coefficients of unicellular LLT polynomials can be expressed as evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements, linking combinatorics and algebra.
Findings
Coefficients are evaluations of Hecke algebra traces
Expressions involve Kazhdan-Lusztig bases and R-polynomials
Provides new formulas connecting LLT polynomials and Hecke algebra
Abstract
We show that coefficients in unicellular LLT polynomials are evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements. We express these in terms of traditional trace bases, induction, and Kazhdan-Lusztig R-polynomials.
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