Generating functions of dual $K$-theoretic $P$- and $Q$-functions and boson-fermion correspondence

Shinsuke Iwao

Published 2023-01-30Version 1

We provide a new description of the dual $K$-theoretic $P$- and $Q$-functions in terms of the boson-fermion correspondence. Our result generalizes the neutral-fermionic presentation of the Schur $P$- and $Q$-functions. As a corollary, we derive a generating function of the dual $K$-theoretic $Q$-function $gq_\lambda$, which was conjectured by Nakagawa-Naruse. We also present a generating function of the dual $K$-theoretic $P$-function $gp_\lambda$.