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, 2016, том 12,002, 172 стр.

Эта публикация цитируется в 12 статьях

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. Kirillov^abc

^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

Аннотация: We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang–Baxter equations.

Ключевые слова: 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.

MSC: 14N15; 53D45; 16W30

Поступила: 23 марта 2015 г.; в окончательном варианте 27 декабря 2015 г.; опубликована 5 января 2016 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2016.002