Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655374 | Journal of Combinatorial Theory, Series A | 2014 | 15 Pages |
Abstract
Let C denote the field of complex numbers, and fix a nonzero qâC such that q4â 1. Define a C-algebra Îq by generators and relations in the following way. The generators are A, B, C. The relations assert that each ofA+qBCâqâ1CBq2âqâ2,B+qCAâqâ1ACq2âqâ2,C+qABâqâ1BAq2âqâ2 is central in Îq. The algebra Îq is called the universal Askey-Wilson algebra. Let Î denote a distance-regular graph that has q-Racah type. Fix a vertex x of Î and let T=T(x) denote the corresponding subconstituent algebra. In this paper we discuss a relationship between Îq and T. Assuming that every irreducible T-module is thin, we display a surjective C-algebra homomorphism ÎqâT. This gives a Îq action on the standard module of T.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Paul Terwilliger, Arjana Žitnik,