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

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 a 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 which 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.