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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 002, 172 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.002 (Mi sigma1084) 		 
This article is cited in 12 scientific papers (total in 12 papers)

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

Anatol N. Kirillovabc

a Research Institute of Mathematical Sciences (RIMS), Kyoto, Sakyo-ku 606-8502, Japan
b The Kavli Institute for the Physics and Mathematics of the Universe (IPMU), 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
c Department of Mathematics, National Research University Higher School of Economics, 7 Vavilova Str., 117312, Moscow, Russia
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DOI: https://doi.org/10.3842/SIGMA.2016.002
Abstract: We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang–Baxter equations.
Keywords: braid and Yang–Baxter groups; classical and dynamical Yang–Baxter relations; classical Yang–Baxter, Kohno–Drinfeld and $3$-term relations algebras; Dunkl, Gaudin and Jucys–Murphy elements; small quantum cohomology and $K$-theory of flag varieties; Pieri rules; Schubert, Grothendieck, Schröder, Ehrhart, Chromatic, Tutte and Betti polynomials; reduced polynomials; Chan–Robbins–Yuen polytope; $k$-dissections of a convex $(n+k+1)$-gon, Lagrange inversion formula and Richardson permutations; multiparameter deformations of Fuss–Catalan and Schröder polynomials; Motzkin, Riordan, Fine, poly-Bernoulli and Stirling numbers; Euler numbers and Brauer algebras; VSASM and CSTCPP; Birman–Ko–Lee monoid; Kronecker elliptic sigma functions.
Received: March 23, 2015; in final form December 27, 2015; Published online January 5, 2016
Bibliographic databases:
Document Type: Article
MSC: 14N15; 53D45; 16W30
Language: English
Citation: Anatol N. Kirillov, “On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss–Catalan, Universal Tutte and Reduced Polynomials”, SIGMA, 12 (2016), 002, 172 pp.
Citation in format AMSBIB
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\by Anatol~N.~Kirillov
\paper On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss--Catalan, Universal Tutte and Reduced Polynomials
\jour SIGMA
\yr 2016
\vol 12
\papernumber 002
\totalpages 172
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    • This publication is cited in the following 12 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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