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

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.

Dedicated to the memory of Alain Lascoux (1944-2013). Preprint RIMS-1817, 172 pages

References in corpus (4)

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• Notes on Schubert, Grothendieck and Key Polynomials
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• Free-fermions and skew stable Grothendieck polynomials
• A Murnaghan-Nakayama rule for Grothendieck polynomials of Grassmannian type
• Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation
• $t$-Unique Reductions for Mészáros's Subdivision Algebra
• Odd supersymmetrization of elliptic R-matrices
• Odd supersymmetric Kronecker elliptic function and Yang-Baxter equations