Boson-fermion correspondence for Hall-Littlewood polynomials revisited

Abstract

We connect twisted vertex operator presentation of Hall-Littlewood polynomials with the action of charged free fermions, describe a boson-fermion correspondence that relates twisted vertex operators with classical Heisenberg algebra. We also show that the elements of the orthogonal to Schur functions basis of the one-parameter deformation of the ring of symmetric functions $\Lambda[t]$ are $\tau$-functions of KP hierarchy.