Free-fermions and skew stable Grothendieck polynomials

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) stabl...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2022-09, Vol.56 (2), p.493-526
Main Author: Iwao, Shinsuke
Format: Article
Language:English
Subjects:
Combinatorial analysis
Combinatorics
Computer Science
Convex and Discrete Geometry
Fermions
Group Theory and Generalizations
Lattices
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiplication
Order
Ordered Algebraic Structures
Polynomials
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Summary: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.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-022-01121-6