Geodesic
Hilbert Series of Typical Representations for Lie Superalgebras
Alexander Heaton1, 2 ; Songpon Sriwongsa3
1Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
2Technische Universität, Berlin, Germany
3Dept. of Mathematics, Center in Theoretical and Comp. Science, Faculty of Science, King Mongkut's University of Technology, Thonburi, Bangkok, Thailand
Journal of Lie Theory, Tome 31 (2021) no. 3, pp. 797-809

Voir la notice de l'article provenant de la source Heldermann Verlag

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 finite-dimensional irreducible typical g-representations. 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.
Classification : 17B10, 05E10, 20C35
Mots-clés : Hilbert series, projective embedding, typical representations

Alexander Heaton  1 , 2   ; Songpon Sriwongsa  3

1 Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
2 Technische Universität, Berlin, Germany
3 Dept. of Mathematics, Center in Theoretical and Comp. Science, Faculty of Science, King Mongkut's University of Technology, Thonburi, Bangkok, Thailand 
Alexander Heaton; Songpon Sriwongsa. Hilbert Series of Typical Representations for Lie Superalgebras. Journal of Lie Theory, Tome 31 (2021) no. 3, pp. 797-809. http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a7/
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     author = {Alexander Heaton and Songpon Sriwongsa},
     title = {Hilbert {Series} of {Typical} {Representations} for {Lie} {Superalgebras}},
     journal = {Journal of Lie Theory},
     pages = {797--809},
     year = {2021},
     volume = {31},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a7/}
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