Infinite rank spinor and oscillator representations

TL;DR

This paper develops a functorial framework for infinite rank spinor and oscillator representations, extending Schur functor theory to orthogonal and symplectic groups, with models and calculations for finite rank specializations.

Contribution

It introduces a new categorical approach to infinite rank spinor and oscillator representations, including models and derived functor calculations.

Findings

Defined a category of representations for infinite rank pin and metaplectic groups

Provided three models: multilinear algebra, diagram categories, twisted Lie algebras

Calculated derived functors for specialization to finite rank groups

Abstract

We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As such, there are a few main points in common. We define a category of representations of what might be thought of as the infinite rank pin and metaplectic groups, and give three models of this category in terms of: multilinear algebra, diagram categories, and twisted Lie algebras. We also define specialization functors to the finite rank groups and calculate the derived functors.