Journal of Lie Theory

no. 3
Hilbert Series of Typical Representations for Lie Superalgebras
Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 797-809
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.
DOI: 10.5802/jolt.1195
Classification: 17B10, 05E10, 20C35
Keywords: Hilbert series, projective embedding, typical representations 
@article{JOLT_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},
     doi = {10.5802/jolt.1195},
     zbl = {1492.17009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1195/}
}
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%A S. Sriwongsa
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%J Journal of Lie Theory
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A. Heaton; S. Sriwongsa. Hilbert Series of Typical Representations for Lie Superalgebras. Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 797-809. doi: 10.5802/jolt.1195

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