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 Schubert class in the $K$-theory coherent sheaves on Lagrangian Grassmannian. Our provides simple description and yields straightforward proof two types Pfaffian formulas for them. present dual space $G\Gamma$, vector generated by all constructing non-degenerate bilinear form that is compatible with neutral fermionic presentation. give family their presentations, formulas.