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Towards categorification of boson-fermion correspondence

SPEAKER: Vera Serganova

TITLE: Towards categorification of boson-fermion correspondence

ABSTRACT: The boson-fermion correspondence relates the actions of the infinite-dimensional Clifford algebra and the infinite-dimensional Heisenberg algebra in the so-called Fock space. It is an important tool in physics but it also has many applications in representation theory and combinatorics. In particular, symmetric functions and Schur polynomials appear very naturally in this setting.

We propose to identify the Fock space with the Grothendieck ring of a certain category of representations over the Lie algebra sl(infinity) and then realize the generators of Clifford and Heisenberg algebra in terms of functors in the corresponding derived category. This realization gives a non-computational categorical proof for certain identities of vertex operators.

Joint work with Igor Frenkel and Ivan Penkov.