
Journal of Lie Theory 31 (2021), No. 3, 797809 Copyright Heldermann Verlag 2021 Hilbert Series of Typical Representations for Lie Superalgebras Alexander Heaton Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany and: Technische Universität, Berlin, Germany heaton@mis.mpg.de Songpon Sriwongsa Dept. of Mathematics, and: Center in Theoretical and Comp. Science, Faculty of Science, King Mongkut's University of Technology, Thonburi, Bangkok, Thailand songpon.sri@kmutt.ac.th Let g be a basic classical Lie superalgebra over the complex numbers C. In the case of a typical weight whose every nonnegative integer multiple is also typical, we compute a closed form for the Hilbert series whose coefficients encode the dimensions of finitedimensional irreducible typical grepresentations. We give a formula for this Hilbert series in terms of elementary symmetric polynomials and Eulerian polynomials. Additionally, we show a simple closed form in terms of differential operators. Keywords: Hilbert series, projective embedding, typical representations. MSC: 17B10, 05E10, 20C35. [ Fulltextpdf (136 KB)] for subscribers only. 