Distributions defined by \(q\)-supernomials, fusion products, and Demazure modules

zbMath1308.05012arXiv1209.1748MaRDI QIDQ2260630

Ernst Schulte-Geers, Stavros Kousidis

Publication date: 11 March 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.1748

zbMATH Keywords

asymptotic normalitycentral limit theoremcurrent algebramixing distributionaffine Kac-Moody algebraDemazure modulefusion productlocal central limit theorem\(q\)-supernomialbasic specializationoccupancy statistic

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Representation theory of lattices (06B15) Asymptotic enumeration (05A16) Probability theory on algebraic and topological structures (60B99)

Uses Software

• MahonianStat

Cites Work

• Expected degree of weights in Demazure modules of \({\widehat{\mathfrak{sl}}_2}\)
• An enumeration of flags in finite vector spaces
• Generalized Galois numbers, inversions, lattice paths, ferrers diagrams and limit theorems
• The Mahonian probability distribution on words is asymptotically normal
• Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers
• Weyl, Demazure and fusion modules for the current algebra of \(\mathfrak{sl}_{r+1}\)
• Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions
• A theorem on the fixed point set of a unipotent transformation of the flag manifold
• Supernomial coefficients, polynomial identities and \(q\)-series
• Character formulae of \(\widehat{\text{sl}}_n\)-modules and inhomogeneous paths
• Inhomogeneous lattice paths, generalized Kostka polynomials and \(A_{n-1}\) supernomials
• Some asymptotic formulas for lattice paths
• The number of flags in finite vector spaces: asymptotic normality and Mahonian statistics
• Asymptotics of generalized Galois numbers via affine Kac-Moody algebras
• ON THE LAW OF LARGE NUMBERS FOR DEMAZURE MODULES OF $\widehat{\mathfrak{sl}}_2$
• On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other
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