Neutral-fermionic presentation of the $K$-theoretic $Q$-function
Abstract
We show a new neutral-fermionic presentation of Ikeda-Naruse's -theoretic -functions, which represent a Schubert class in the -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 , the vector space generated by all -theoretic -functions, by constructing a non-degenerate bilinear form that is compatible with the neutral fermionic presentation. We give a new family of dual -theoretic -functions, their neutral-fermionic presentations, and Pfaffian formulas.
Keywords
Cite
@article{arxiv.1904.02279,
title = {Neutral-fermionic presentation of the $K$-theoretic $Q$-function},
author = {Shinsuke Iwao},
journal= {arXiv preprint arXiv:1904.02279},
year = {2021}
}
Comments
27 pages, 1 figure v4: Major revision. The title has been changed. (The old title was "Pfaffian formulas in K-theory and the Boson-Fermion Correspondence")