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On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials
Інший ID:
2010 Mathematics Subject Classification: 14N15; 53D45; 16W30
DOI:10.3842/SIGMA.2016.002
DOI:10.3842/SIGMA.2016.002
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
664
Завантажень:
333
Анотація:
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations.
