258 citations · 748 across the 60 of their papers we have counts for
16 papers · 1 filter
Bethe subalgebras in Hecke algebra and Gaudin models
A. P. Isaev, Anatol N. Kirillov
The generating function for elements of the Bethe subalgebra of Hecke algebra is constructed as Sklyanin's transfer-matrix operator for Hecke chain. We show that in a special class…
Affine nil-Hecke algebras and braided differential structure on affine Weyl groups
Anatol N. Kirillov, Toshiaki Maeno
We construct a model of the affine nil-Hecke algebra as a subalgebra of the Nichols-Woronowicz algebra associated to a Yetter-Drinfeld module over the affine Weyl group. We also di…
Generalized Energy Statistics and Kostka--Macdonald Polynomials
Anatol N. Kirillov, Reiho Sakamoto
We give an interpretation of the t=1 specialization of the modified Macdonald polynomial as a generating function of the energy statistics defined on the set of paths arising in th…
Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations
Anatol N. Kirillov, Reiho Sakamoto
There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba--Takagi--Takeno…
Paths and Kostka--Macdonald Polynomials
Anatol N. Kirillov, Reiho Sakamoto
We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight mu…
Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties
Anatol N. Kirillov, Toshiaki Maeno
For the root system of type we introduce and study a certain extension of the quadratic algebra invented by S. Fomin and the first author, to construct a model for the equivari…