Polynomial functors and categorifications of Fock space

Abstract

Fix an infinite field $k$ of characteristic $p$, and let $\g$ be the Kac-Moody algebra ${\mathfrak{sl}}_{\infty }$ if $p=0$ and ${\widehat{\mathfrak{sl}}}_p$ otherwise. Let $\PP$ denote the category of strict polynomial functors defined over $k$. We describe a $\g$-action on $\PP$ (in the sense of Chuang and Rouquier) categorifying the Fock space representation of $\g$.

23 pages

References in corpus (2)

• 2-Kac-Moody algebras
• Polynomial representations and categorifications of Fock Space

Cited by in corpus (1)

• A categorification of the boson-fermion correspondence via representation theory of $sl(\infty)