2007/11/21 by Cédric Lecouvey, Cedric Lecouvey, Lecouvey, Cedric +2
Mathematics · #17B10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B10
paper · pdf · doi:10.48550/arxiv.0711.3433
16 pages, 1 figure
openalex publication_date 2007/11/21 · arxiv created 2008/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is devoted to the generalization of Lusztig's q-analog of weight multiplicities to the Lie superalgebras gl(n,m) and spo(2n,M). We define such q-analogs Klambda,mu(q) for the typical modules and for the irreducible covariant tensor gl(n,m)-modules of highest weight lambda. For gl(n,m), the defined polynomials have nonnegative integer coefficients if the weight mu is dominant. For spo(2n,M), we show that the positivity property holds when mu is dominant and sufficiently far from a specific wall of the fundamental chamber. We also establish that the q-analog associated to an irreducible covariant tensor gl(n,m)-module of highest weight lambda and a dominant weight mu is the generating series of a simple statistic on the set of semistandard hook-tableaux of shape lambda and weight mu. This statistic can be regarded as a super analog of the charge statistic defined by Lascoux and Schutzenberger.