Skip to main content

Enumeration of H-strata in quantum matrices with respect to dimension

Bell, Jason, Casteels, Karel L, Launois, Stephane (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. (doi:10.1016/j.jcta.2011.07.007) (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) (KAR id:28765)

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.
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
DOI/Identification number: 10.1016/j.jcta.2011.07.007
Uncontrolled keywords: Combinatorics; Representation theory; Quantum groups
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 20 Feb 2012 11:28 UTC
Last Modified: 16 Nov 2021 10:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/28765 (The current URI for this page, for reference purposes)

University of Kent Author Information

Casteels, Karel L.

Creator's ORCID:
CReDIT Contributor Roles:

Launois, Stephane.

Creator's ORCID: https://orcid.org/0000-0001-7252-8515
CReDIT Contributor Roles:
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.