Bell, Jason and Launois, Stephane and 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. (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)
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).
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Stephane Launois|
|Date Deposited:||29 Jun 2011 13:09|
|Last Modified:||28 May 2014 10:54|
|Resource URI:||https://kar.kent.ac.uk/id/eprint/23432 (The current URI for this page, for reference purposes)|