7 citations · 10 across the 5 of their papers we have counts for
13 papers
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…
Exterior differential algebras and flat connections on Weyl groups
Anatol N. Kirillov, Toshiaki Maeno
We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group…
Hypergeometric Generating Function of L-function, Slater's Identities, and Quantum Invariant
Kazuhiro Hikami, Anatol N. Kirillov
We study certain connections between the quantum invariants of the torus knots T_{3,2^k} and some q-series identities. In particular, we obtain new generalizations of Slater's iden…
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…