On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials

TL;DR

This paper explores the combinatorial and algebraic properties of quadratic algebras connected to Yang-Baxter equations, focusing on Dunkl, Gaudin, and various polynomial structures.

Contribution

It introduces new insights into the structure of quadratic algebras related to integrable systems and combinatorics, expanding understanding of their algebraic and combinatorial properties.

Findings

Identification of algebraic relations in quadratic algebras

Connections between algebraic structures and combinatorial polynomials

New properties of Dunkl and Gaudin elements

Abstract

We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.