A Categorification of the Spin Representation of $U(\mf{so}(7,\C))$ via Projective Functors

TL;DR

This paper develops a categorification of the tensor powers of the spin representation of the Lie algebra {so}(7,\u2102) using projective functors in the BGG category of {gl}_n, linking representation theory and categorification.

Contribution

It introduces a novel categorification approach for the spin representation tensor powers via singular blocks and projective functors in the BGG category.

Findings

Establishes a categorification framework for the spin representation tensor powers.

Connects the representation theory of {so}(7,) with categorification techniques.

Provides new insights into the structure of the BGG category for {gl}_n.

Abstract

The purpose of this paper is to study a categorification of the $n$-th tensor power of the spin representation of $U(\mf{so}(7,\C))$ by using certain singular blocks and projective functors of the BGG category of the complex Lie algebra $\mf{gl}_n$.