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

@article{citeulike:3986072, 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\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).}, archivePrefix = {arXiv}, author = {Bell, J. and Launois, S. and Lutley, J.}, citeulike-article-id = {3986072}, citeulike-linkout-0 = {http://arxiv.org/abs/0901.4707}, citeulike-linkout-1 = {http://arxiv.org/pdf/0901.4707}, eprint = {0901.4707}, keywords = {algebra, automata, combinatorics, computation, mathematics, quantum}, month = {Jan}, posted-at = {2009-01-30 17:38:21}, priority = {2}, title = {An automaton-theoretic approach to the representation theory of quantum algebras}, url = {http://arxiv.org/abs/0901.4707}, year = {2009} }

TY - JOUR ID - citeulike:3986072 L3 - citeulike-article-id:3986072 N2 - 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). TI - An automaton-theoretic approach to the representation theory of quantum algebras KW - algebra KW - automata KW - combinatorics KW - computation KW - mathematics KW - quantum AU - Bell, J AU - Launois, S AU - Lutley, J PY - 2009/Jan/29/ UR - http://arxiv.org/abs/0901.4707 ER -