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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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) , Bell, Launois and Lutley (2010) ) regarding the asymptotic proportion of d-dimensional H-strata in Q(q)(M(m,n) (K)).
|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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