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.