On the Subregular J-ring of Coxeter Systems
| dc.contributor.advisor | Ostrik, Victor | |
| dc.contributor.author | Xu, Tianyuan | |
| dc.date.accessioned | 2017-09-06T21:54:04Z | |
| dc.date.available | 2017-09-06T21:54:04Z | |
| dc.date.issued | 2017-09-06 | |
| dc.description.abstract | 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. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/22741 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | Coxeter groups | en_US |
| dc.subject | Fusion categories | en_US |
| dc.subject | Hecke algebras | en_US |
| dc.subject | Kazhdan-Lusztig theory | en_US |
| dc.subject | Partition quantum groups | en_US |
| dc.subject | Tensor categories | en_US |
| dc.title | On the Subregular J-ring of Coxeter Systems | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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