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Polynomial functors and categorifications of Fock space

  • Jiuzu HongEmail author
  • Antoine Touzé
  • Oded Yacobi
Chapter
Part of the Progress in Mathematics book series (PM, volume 257)

Abstract

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

Keywords

Categorification Fock space 

Mathematics Subject Classification:

18D05 17B67 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.LAGA Institut GaliléeUniversité Paris 13VilletaneuseFrance
  3. 3.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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