Suppose that for each we have a representation of the symmetric group . 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 can be given a suitable module structure over a twisted commutative algebra then the sequence 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: 10.5802/alco.9
@article{ALCO_2018__1_1_147_0, author = {Sam, Steven V and Snowden, Andrew}, title = {Hilbert series for twisted commutative algebras}, journal = {Algebraic Combinatorics}, pages = {147--172}, publisher = {MathOA foundation}, volume = {1}, number = {1}, year = {2018}, doi = {10.5802/alco.9}, zbl = {06882338}, mrnumber = {3857163}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.9/} }
TY - JOUR AU - Sam, Steven V AU - Snowden, Andrew TI - Hilbert series for twisted commutative algebras JO - Algebraic Combinatorics PY - 2018 SP - 147 EP - 172 VL - 1 IS - 1 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.9/ DO - 10.5802/alco.9 LA - en ID - ALCO_2018__1_1_147_0 ER -
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. http://archive.numdam.org/articles/10.5802/alco.9/
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