Some generalizations of Schur functors

Sam, Steven; Snowden, Andrew

doi:10.1090/proc/14205

Some generalizations of Schur functors
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by Steven V Sam and Andrew Snowden PDF

Proc. Amer. Math. Soc. 147 (2019), 77-90 Request permission

Abstract:

The theory of Schur functors provides a powerful and elegant approach to the representation theory of $\mathbf {GL}_n$—at least to the so-called polynomial representations—especially to questions about how the theory varies with $n$. We develop parallel theories that apply to other classical groups and to nonpolynomial representations of $\mathbf {GL}_n$. These theories can also be viewed as linear analogs of the theory of $\mathbf {FI}$-modules.

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