Combinatorial $B_n$-analogues of Schubert polynomials
Sergey Fomin, Anatol N. Kirillov
TL;DR
This paper constructs combinatorial analogues of Schubert polynomials for type B_n using solutions to the Yang-Baxter equation involving the nilCoxeter algebra, advancing algebraic combinatorics.
Contribution
It introduces new combinatorial $B_n$-analogues of Schubert polynomials derived from algebraic solutions to the Yang-Baxter equation.
Findings
Constructed combinatorial $B_n$-analogues of Schubert polynomials.
Linked these polynomials to solutions of the $B_n$-Yang-Baxter equation.
Provided algebraic framework involving the nilCoxeter algebra.
Abstract
Combinatorial -analogues of Schubert polynomials and corresponding symmetric functions are constructed from an exponential solution of the -Yang-Baxter equation that involves the nilCoxeter algebra of the hyperoctahedral group.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Topics in Algebra · Algebraic structures and combinatorial models