258 citations · 748 across the 60 of their papers we have counts for
61 papers
Elementary Askey-Wilson Functions
J. F. van Diejen, A. N. Kirillov
We present a determinantal evaluation formula for the very-well-poised basic hypergeometric Askey-Wilson function in terms of elementary functions. The formula in questio…
Hook-content formula using excited Young diagrams
Anatol N. Kirillov, Travis Scrimshaw
We construct a hook-content formula and its -analog using excited Young diagrams analogous to Naruse's hook-length formula for skew shapes. Furthermore, we show that our hook-co…
On -deformations of Postnikov-Shapiro algebras
Anatol N. Kirillov, Gleb Nenashev
For any given loopless graph , we introduce - deformations of its Postnikov-Shapiro algebras counting spanning trees, counting spanning forests and - deformations of int…
Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations
A. P. Isaev, A. N. Kirillov, V. O. Tarasov
Commutative sets of Jucys-Murphyelements for affine braid groups of types were defined. Construction of -matrix representations of the affine b…
Bethe's Quantum Numbers And Rigged Configurations
Anatol N. Kirillov, Reiho Sakamoto
We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg…
Rigged Configurations and Catalan, Stretched Parabolic Kostka Numbers and Polynomials: Polynomiality, Unimodality and Log-concavity
A. N. Kirillov
We will look at the Catalan numbers from the {\it Rigged Configurations} point of view originated \cite{Kir} from an combinatorial analysis of the Bethe Ansatz Equations associated…