Hilbert series for twisted commutative algebras
Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 147-172.

Suppose that for each n0 we have a representation M n of the symmetric group S n . Such sequences arise in a wide variety of contexts, and often exhibit uniformity in some way. We prove a number of general results along these lines in this paper: our prototypical theorem states that if {M n } can be given a suitable module structure over a twisted commutative algebra then the sequence {M n } follows a predictable pattern. We phrase these results precisely in the language of Hilbert series (or Poincaré series, or formal characters) of modules over tca’s.

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DOI: https://doi.org/10.5802/alco.9
Classification: 05E05,  13A50
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Sam, Steven V; Snowden, Andrew. Hilbert series for twisted commutative algebras. Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 147-172. doi : 10.5802/alco.9. https://alco.centre-mersenne.org/articles/10.5802/alco.9/

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