Geodesic
Hilbert Series of Typical Representations for Lie Superalgebras
Journal of Lie theory, Tome 31 (2021) no. 3, pp. 797-809
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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 
@article{JLT_2021_31_3_JLT_2021_31_3_a7,
     author = {A. Heaton and S. 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/JLT_2021_31_3_JLT_2021_31_3_a7/}
}
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A. Heaton; S. 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/JLT_2021_31_3_JLT_2021_31_3_a7/