Polynomial Representations of General Linear Groups and Categorifications of Fock Space

Details Polynomial Representations of General Linear Groups and Categorifications of Fock Space Polynomial Representations of General Linear Groups and Categorifications of Fock Space

2011-01-12

arxiv.org/abs/1101.2456v2

Mathematics

Representation Theory

32 pages, added remarks/references related to the category of strict polynomial functors of finite degree

Scientific paper

We study a limit category $M$ constructed from the polynomial representations of all general linear groups. We construct a $g$-categorification on $M$ in the sense of Chuang and Rouquier, which categorifies the Fock space representation of $g$, (here $g$ is either $\hat{sl}_p$ or $sl_{\infty}$ depending on the characteristic of the ground field). As an application, we construct the Misra-Miwa crystal of Fock space from the set of simple objects of $M$.

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