7 citations · 10 across the 5 of their papers we have counts for
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On some noncommutative algebras related to K-theory of flag varieties, part I
Anatol N. Kirillov, Toshiaki Maeno
For any Lie algebra of classical type or type we define a -theoretic analog of Dunkl's elements, the so-called truncated {\it Ruijsenaars-Schneider-Macdonald elements}, $R…
An Invitation to the Generalized Saturation Conjecture
Anatol N. Kirillov
We report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and ``satu…
Noncommutative algebras related with Schubert calculus on Coxeter groups
Anatol N. Kirillov, Toshiaki Maeno
For any finite Coxeter system we construct a certain noncommutative algebra, so-called {\it bracket algebra}, together with a familiy of commuting elements, so-called {\it…
Generalized Umemura polynomials and Hirota-Miwa equations
Anatol N. Kirillov, Makoto Taneda
We introduce and study generalized Umemura polynomials which are the natural generalization of the Umemura polynomials related to the Painle…
Generalized Umemura polynomials
Anatol N. Kirillov, Makoto Taneda
We introduce and study generalized Umemura polynomials which are a natural generalization of the Umemura polynomials related to Painlevé $VI…
A bijection between Littlewood-Richardson tableaux and rigged configurations
Anatol N. Kirillov, Anne Schilling, Mark Shimozono
A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particl…