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
Joint work with Igor Frenkel and Ivan Penkov.