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

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 $\mf{gl}_n$.