Two non-nilpotent linear transformations that satisfy the cubic $q$-Serre relations
| dc.creator | Ito, Tatsuro | |
| dc.creator | Terwilliger, Paul | |
| dc.date | 2005-08-21 | |
| dc.date.accessioned | 2026-07-07T05:22:33Z | |
| dc.date.available | 2026-07-07T05:22:33Z | |
| dc.description | Let $K$ denote an algebraically closed field with characteristic 0, and let $q$ denote a nonzero scalar in $K$ that is not a root of unity. Let $A_q$ denote the unital associative $K$-algebra defined by generators $x,y$ and relations x^3y-[3]_q x^2yx +[3]_q xyx^2 -yx^3=0, y^3x-[3]_q y^2xy +[3]_q yxy^2 -xy^3=0, where $[3]_q = (q^3-q^{-3})/(q-q^{-1})$. We classify up to isomorphism the finite-dimensional irreducible $A_q$-modules on which neither of $x,y$ is nilpotent. We discuss how these modules are related to tridiagonal pairs. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508398 | |
| dc.identifier | http://arxiv.org/abs/math/0508398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76103 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B37; 05E30, 05E35, 33D45, 33D80 | |
| dc.title | Two non-nilpotent linear transformations that satisfy the cubic $q$-Serre relations | |
| dc.type | text |