Bell, J. and Casteels, K. and Launois, S.
(2012)
*Enumeration of H-strata in quantum matrices with respect to dimension.*
Journal of Combinatorial Theory, Series A, 119
(1).
pp. 83-98.
ISSN 0097-3165.
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Official URL http://dx.doi.org/10.1016/j.jcta.2011.07.007 |

## Abstract

We present a combinatorial method to determine the dimension of H-strata in the algebra of m x n quantum matrices O(q)(M(m,n)(K)) as follows. To a given H-stratum we associate a certain permutation via the notion of pipe dreams. We show that the dimension of the H-stratum is precisely the number of odd cycles in this permutation. Using this result, we are able to give closed formulas for the trivariate generating function that counts the d-dimensional H-strata in Q(q)(M(m,n)(K)). Finally, we extract the coefficients of this generating function in order to settle conjectures proposed by the first and third named authors (Bell and Launois (2010) [3], Bell, Launois and Lutley (2010) [4]) regarding the asymptotic proportion of d-dimensional H-strata in Q(q)(M(m,n) (K)).

Item Type: | Article |
---|---|

Uncontrolled keywords: | Combinatorics; Representation theory; Quantum groups |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |

Depositing User: | Stephane Launois |

Date Deposited: | 20 Feb 2012 11:28 |

Last Modified: | 16 Nov 2012 10:57 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/28765 (The current URI for this page, for reference purposes) |

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