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SIGMA, 2016, Volume 12, 002, 172 pages (Mi sigma1084)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.3842/SIGMA.2016.002

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Bibliographic databases:

ArXiv: 1502.00426
MSC: 14N15; 53D45; 16W30
Received: March 23, 2015; in final form December 27, 2015; Published online January 5, 2016
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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
\Bibitem{Kir16}
\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
\mathnet{http://mi.mathnet.ru/sigma1084}
\crossref{https://doi.org/10.3842/SIGMA.2016.002}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84955066986}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. Matsumura, “An algebraic proof of determinant formulas of Grothendieck polynomials”, Proc. Jpn. Acad. Ser. A-Math. Sci., 93:8 (2017), 82–85  crossref  mathscinet  zmath  isi
    2. T. Hudson, T. Matsumura, “Vexillary degeneracy loci classes in $K$-theory and algebraic cobordism”, Eur. J. Comb., 70 (2018), 190–201  crossref  mathscinet  zmath  isi
    3. D. Grinberg, “$t$-Unique Reductions for Mészáros's Subdivision Algebra”, SIGMA, 14 (2018), 078, 34 pp.  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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