TY - JOUR
T1 - Free-fermions and skew stable Grothendieck polynomials
AU - Iwao, Shinsuke
N1 - Funding Information:
This work is partially supported by JSPS Kakenhi Grant Number 19K03605. The author is grateful to Professor Takeshi Ikeda for his comments on the manuscript and for his suggestions for future research.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/9
Y1 - 2022/9
N2 - We present a free-fermionic presentation of the skew (dual) stable Grothendieck polynomials. A direct proof of their determinantal formulas is given from this presentation. We also introduce a combinatorial method to describe the multiplication map and its adjoint over the space of skew (dual) stable Grothendieck polynomials. This calculation requires the use of noncommutative supersymmetric Schur functions.
AB - We present a free-fermionic presentation of the skew (dual) stable Grothendieck polynomials. A direct proof of their determinantal formulas is given from this presentation. We also introduce a combinatorial method to describe the multiplication map and its adjoint over the space of skew (dual) stable Grothendieck polynomials. This calculation requires the use of noncommutative supersymmetric Schur functions.
KW - Boson–fermion correspondence
KW - Determinantal formula
KW - Noncommutative supersymmetric Schur function
KW - Skew stable Grothendieck polynomial
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U2 - 10.1007/s10801-022-01121-6
DO - 10.1007/s10801-022-01121-6
M3 - Article
AN - SCOPUS:85127590260
SN - 0925-9899
VL - 56
SP - 493
EP - 526
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 2
ER -