On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations.
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| Datum: | 2016 |
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| Sprache: | English |
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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Zitieren: | On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 142 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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oai:nasplib.isofts.kiev.ua:123456789-1474192025-02-23T17:11:07Z On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials Kirillov, A.N. We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. I would like to express my deepest thanks to Professor Toshiaki Maeno for many years fruitful collaboration. I’m also grateful to Professors Yu. Bazlov, I. Burban, B. Feigin, S. Fomin, A. Isaev, M. Ishikawa, M. Noumi, B. Shapiro and Dr. Evgeny Smirnov for fruitful discussions on dif ferent stages of writing [72]. My special thanks are to Professor Anders Buch for sending me the programs for computation of the β-Grothendieck and double β-Grothendieck polynomials. Many results and examples in the present paper have been checked by using these programs, and Professor Ole Warnaar (University of Queenslad) for a warm hospitality and a kind interest and fruitful discussions of some results from [72] concerning hypergeometric functions. 2016 Article On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 142 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14N15; 53D45; 16W30 DOI:10.3842/SIGMA.2016.002 https://nasplib.isofts.kiev.ua/handle/123456789/147419 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. |
| format |
Article |
| author |
Kirillov, A.N. |
| spellingShingle |
Kirillov, A.N. On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kirillov, A.N. |
| author_sort |
Kirillov, A.N. |
| title |
On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials |
| title_short |
On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials |
| title_full |
On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials |
| title_fullStr |
On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials |
| title_full_unstemmed |
On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials |
| title_sort |
on some quadratic algebras i 1/2: combinatorics of dunkl and gaudin elements, schubert, grothendieck, fuss-catalan, universal tutte and reduced polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| citation_txt |
On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 142 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-22T04:09:54Z |
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2025-07-22T04:09:54Z |
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1838318768132980736 |