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arXiv · 1705.10718

Hilbert series for twisted commutative algebras

Steven V Sam·Andrew Snowden
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Abstract

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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Steven V Sam, Andrew Snowden. 2018-01-31. Hilbert series for twisted commutative algebras. https://doi.org/10.5802/alco.9

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