TY - JOUR
T1 - Neutral-fermionic presentation of the K-theoretic Q-function
AU - Iwao, Shinsuke
N1 - Funding Information:
This work is partially supported by JSPS Kakenhi Grant Number 19K03605. The author is very grateful to Prof. Takeshi Ikeda for his valuable advice. The author also would like to thank Prof. Hiroshi Naruse for important suggestions on the manuscript.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - Boson-Fermion correspondence
KW - K-theoretic Q-functions
KW - Neutral fermions
KW - Pfaffian formulas
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U2 - 10.1007/s10801-021-01064-4
DO - 10.1007/s10801-021-01064-4
M3 - Article
AN - SCOPUS:85115673989
SN - 0925-9899
VL - 55
SP - 629
EP - 662
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 2
ER -