Neutral-fermionic presentation of the $K$-theoretic $Q$-function

Abstract

We show a new neutral-fermionic presentation of Ikeda-Naruse's $K$-theoretic $Q$-functions, which represent a Schubert class in the $K$-theory of coherent sheaves on the Lagrangian Grassmannian. Our presentation provides a simple description and yields straightforward proof of two types of Pfaffian formulas for them. We present a dual space of $G\Gamma$, the vector space generated by all $K$-theoretic $Q$-functions, by constructing a non-degenerate bilinear form that is compatible with the neutral fermionic presentation. We give a new family of dual $K$-theoretic $Q$-functions, their neutral-fermionic presentations, and Pfaffian formulas.

27 pages, 1 figure v4: Major revision. The title has been changed. (The old title was "Pfaffian formulas in K-theory and the Boson-Fermion Correspondence")

References in corpus (1)

• Integrability approach to Feher-Nemethi-Rimanyi-Guo-Sun type identities for factorial Grothendieck polynomials

Cited by in corpus (2)

• Free fermions and Schur expansions of multi-Schur functions
• Shifted combinatorial Hopf algebras from $K$-theory