2015/08/04 by Matthew Bennett, Bennett, Matthew, Rollo Jenkins +1
Mathematics · Physics and Astronomy · #17B10 #17B70 #20C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B70 #msc:20C30
paper · pdf · doi:10.48550/arxiv.1508.00941
openalex publication_date 2015/08/04 · arxiv created 2015/09/10 · arxiv updated 2015/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite-dimensional module, V, for a finite-dimensional, complex, semi-simple Lie algebra \lie g and a positive integer m, we construct a family of graded modules for the current algebra \lie g[t] indexed by simple \CC\lie Sm-modules. These modules have the additional structure of being free modules of finite rank for the ring of symmetric polynomials and so can be localized to give finite-dimensional graded \lie g[t]-modules. We determine the graded characters of these modules and show that if \lie g is of type A and V the natural representation, these graded characters admit a curious duality.