Let (W, S) be an arbitrary Coxeter system, and let J be the asymptotic Hecke
algebra associated to (W, S) via Kazhdan-Lusztig polynomials by Lusztig. We study
a subalgebra J_C of J corresponding to the subregular cell C of W . We prove a
factorization theorem that allows us to compute products in J_C without inputs
from Kazhdan-Lusztig theory, then discuss two applications of this result. First, we
describe J_C in terms of the Coxeter diagram of (W, S) in the case (W, S) is simply-
laced, and deduce more connections between the diagram and J_C in some other
cases. Second, we prove that for certain specific Coxeter systems, some subalgebras
of J_C are free fusion rings, thereby connecting the algebras to compact quantum
groups arising in operator algebra theory.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/22741 |
| Date | 06 September 2017 |
| Creators | Xu, Tianyuan |
| Contributors | Ostrik, Victor |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Rights | All Rights Reserved. |
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