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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147419 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862529275383513088 |
|---|---|
| author | Kirillov, A.N. |
| author_facet | Kirillov, A.N. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations.
|
| first_indexed | 2025-11-24T02:39:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147419 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T02:39:40Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kirillov, A.N. 2019-02-14T18:13:23Z 2019-02-14T18:13:23Z 2016 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 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials Article published earlier |
| spellingShingle | 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. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147419 |
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