The shape of a tridiagonal pair
| dc.creator | Ito, Tatsuro | |
| dc.creator | Terwilliger, Paul | |
| dc.date | 2003-04-17 | |
| dc.date.accessioned | 2026-07-07T04:57:00Z | |
| dc.date.available | 2026-07-07T04:57:00Z | |
| dc.description | Let K denote an algebraically closed field with characteristic 0. Let V denote a vector space over K with finite positive dimension and let A,B denote a tridiagonal pair on V. We make an assumption about this pair. Let q denote a nonzero scalar in K which is not a root of unity. We assume A and B satisfy the q-Serre relations (i) A^3B - [3]A^2BA + [3]ABA^2 - BA^3=0; (ii) B^3A - [3]B^2AB + [3]BAB^2 - AB^3=0, where [3]=(q^3-q^{-3})/(q-q^{-1}). Let (ρ_0, ρ_1,...,ρ_d) denote the shape vector for A,B. We show the entries in this shape vector are bounded above by binomial coefficients. Indeed we show ρ_i is at most (d \atop i) for 0 \leq i \leq d. We obtain this result by displaying a spanning set for V. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304244 | |
| dc.identifier | http://arxiv.org/abs/math/0304244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67124 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B37; 05E35, 33C45, 33D45 | |
| dc.title | The shape of a tridiagonal pair | |
| dc.type | text |