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 combinatorics. We show that for a fixed number m, the torus-invariant primitive ideals in m × 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 × n quantum matrices satisfies a linear recurrence in n over the rational numbers. In the 3 × 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 ) .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
