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

Shinsuke Iwao

Research output: Contribution to journalArticlepeer-review

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 a straightforward proof of two types of Pfaffian formulas for them. We present a dual space of GΓ, 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.

Original languageEnglish
Pages (from-to)629-662
Number of pages34
JournalJournal of Algebraic Combinatorics
Volume55
Issue number2
DOIs
Publication statusPublished - 2022 Mar
Externally publishedYes

Keywords

  • Boson-Fermion correspondence
  • K-theoretic Q-functions
  • Neutral fermions
  • Pfaffian formulas

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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