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arXiv · 1904.02279

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

Shinsuke Iwao
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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.

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Shinsuke Iwao. 2019-04-04. Neutral-fermionic presentation of the $K$-theoretic $Q$-function. https://doi.org/10.1007/s10801-021-01064-4

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