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 f...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2022-03, Vol.55 (2), p.629-662
Main Author: Iwao, Shinsuke
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Sheaves
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Summary: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 Γ , 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.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-021-01064-4