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Hilbert series for twisted commutative algebras
Sam, Steven V1; Snowden, Andrew2
1 Department of Mathematics, University of Wisconsin, Madison, WI
2 Department of Mathematics, University of Michigan, Ann Arbor, MI
Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 147-172.

Suppose that for each n≥0 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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Accepted:
Published online:
DOI: 10.5802/alco.9
Classification: 05E05, 13A50

Sam, Steven V 1; Snowden, Andrew 2

1 Department of Mathematics, University of Wisconsin, Madison, WI
2 Department of Mathematics, University of Michigan, Ann Arbor, MI
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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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