Some generalizations of Schur functors

TL;DR

This paper extends the theory of Schur functors to other classical groups and non-polynomial representations, providing new frameworks that parallel FI-module theory and enhance understanding of representation variation.

Contribution

It introduces generalized Schur functor theories applicable to various classical groups and non-polynomial representations, expanding the scope of representation theory.

Findings

Developed parallel theories for classical groups

Extended Schur functor applications beyond polynomial representations

Connected to linear analogs of FI-module theory

Abstract

The theory of Schur functors provides a powerful and elegant approach to the representation theory of 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 non-polynomial representations of GL_n. These theories can also be viewed as linear analogs of the theory of FI-modules.