Polynomial representations and categorifications of Fock Space

Abstract

The rings of symmetric polynomials form an inverse system whose limit, the ring of symmetric functions, is the model for the bosonic Fock space representation of the affine Lie algebra. We categorify this construction by considering an inverse limit of categories of polynomial representation of general linear groups. We show that this limit naturally carries an action of the affine Lie algebra (in the sense of Rouquier), thereby obtaining a famiy of categorifications of the bosonic Fock space representation.

32 pages, to appear in Algebras and Representation Theory

References in corpus (3)

• 2-Kac-Moody algebras
• Quiver Schur algebras and q-Fock space
• Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras

Cited by in corpus (5)

• A categorification of the boson-fermion correspondence via representation theory of $sl(\infty)
• Highest weight sl_2-categorifications I: crystals
• Polynomial functors and categorifications of Fock space
• Notes on Restricted Inverse Limits of Categories
• Representations of general linear groups and categorical actions of Kac-Moody algebras