Hilbert series for twisted commutative algebras
Steven V Sam, Andrew Snowden
Source 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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