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An automaton-theoretic approach to the representation theory of quantum algebras

Bell, Jason, Launois, Stephane, Lutley, Jamie (2010) An automaton-theoretic approach to the representation theory of quantum algebras. Advances in Mathematics, 223 (2). pp. 476-510. ISSN 0001-8708. (doi:10.1016/j.aim.2009.08.013) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:23432)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/j.aim.2009.08.013

Abstract

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 combinatories. We show that for a fixed number in, the torus-invariant primitive ideals in m x 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 parameterizes the primes that are torus-invariant, we show that for m fixed, the number P(m, n) of torus-invariant primitive ideals in m x n quantum matrices satisfies a linear recurrence in n over the rational numbers. In the 3 x 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).

Item Type: Article
DOI/Identification number: 10.1016/j.aim.2009.08.013
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 29 Jun 2011 13:09 UTC
Last Modified: 06 May 2020 03:05 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/23432 (The current URI for this page, for reference purposes)
Launois, Stephane: https://orcid.org/0000-0001-7252-8515
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