Categorification of Clifford algebra via geometric induction and restriction

TL;DR

This paper develops a categorification of the Clifford algebra action on Fock space using geometric induction and restriction functors related to supergroups, advancing the understanding of algebraic structures in representation theory.

Contribution

It introduces a novel categorification approach for Clifford algebra actions via geometric methods and supergroup functors, connecting algebraic and geometric representation theories.

Findings

Categorification of Clifford algebra action on Fock space achieved.

Use of geometric parabolic induction functors and supergroup adjoints.

Establishment of a new link between geometric methods and algebraic structures.

Abstract

We use geometric parabolic induction functors and the adjoint functors for the supergroups Osp(2m+1,2n) (where m and n vary) to categorify the action of the infinite-dimensional Clifford algebra on the Fock space of semi-infinite forms.