Free-fermions and canonical Grothendieck polynomials
Shinsuke Iwao, Kohei Motegi, and Travis Scrimshaw
TL;DR
This paper presents a free-fermion framework for refined canonical Grothendieck polynomials, deriving identities and formulas that advance understanding of their algebraic and combinatorial properties.
Contribution
It introduces a novel free-fermion approach to represent and analyze refined canonical Grothendieck polynomials and their skew versions.
Findings
Derived skew Cauchy identities
Established branching rules and expansion formulas
Presented integral formulas for the polynomials
Abstract
We give a presentation of refined (dual) canonical Grothendieck polynomials and their skew versions using free-fermions. Using this, we derive a number of identities, including the skew Cauchy identities, branching rules, expansion formulas, and integral formulas.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models