An automaton-theoretic approach to the representation theory of quantum algebras
| dc.creator | Bell, J. | |
| dc.creator | Launois, S. | |
| dc.creator | Lutley, J. | |
| dc.date | 2009-01-29 | |
| dc.date.accessioned | 2026-07-07T12:35:38Z | |
| dc.date.available | 2026-07-07T12:35:38Z | |
| dc.description | We develop a new approach to the representation theory of quantum algebras supporting a torus action via methods from the theory of finite-state automata and algebraic combinatorics. We show that for a fixed number $m$, the torus-invariant primitive ideals in $m\times n$ quantum matrices can be seen as a regular language in a natural way. Using this description and a semigroup approach to the set of Cauchon diagrams, a combinatorial object that paramaterizes the primes that are torus-invariant, we show that for $m$ fixed, the number of torus-invariant primitive ideals in $m\times n$ quantum matrices satisfies a linear recurrence in $n$ over the rational numbers. In the $3\times n$ case we give a concrete description of the torus-invariant primitive ideals and use this description to give an explicit formula for the number P(3,n). | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/0901.4707 | |
| dc.identifier | http://arxiv.org/abs/0901.4707 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217827 | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | An automaton-theoretic approach to the representation theory of quantum algebras | |
| dc.type | text |