Categorical Bernstein operators and the Boson-Fermion correspondence
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Nicolle S. González [1]
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[1] UCLA, USA
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 4, 2020
- Idioma: inglés
- DOI: 10.1007/s00029-020-00558-6
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Resumen
We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to infinite chain complexes in Khovanov’s Heisenberg category H and from them construct categorical analogues of the Kac-Frenkel fermionic vertex operators. These fermionic functors are then shown to satisfy categorical Clifford algebra relations, solving a conjecture of Cautis and Sussan. We also prove another conjecture of Cautis and Sussan demonstrating that the categorical Fock space representation of H is a direct summand of the regular representation by showing that certain infinite chain complexes are categorical Fock space idempotents. In the process, we enhance the graphical calculus of H by lifting various Littlewood-Richardson branching isomorphisms to the Karoubian envelope of H.
