258 citations · 748 across the 60 of their papers we have counts for
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Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels
Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi
The spectral decomposition of the path space of the vertex model associated to the level representation of the quantized affine algebra is studied. The spectr…
Domino tableaux, Schutzenberger involution, and the symmetric group action
Arkady Berenstein, Anatol N. Kirillov
We define an action of the symmetric group on the set of domino tableaux, and prove that the number of domino tableaux of a given weight does not depend on the permutation of compo…
On some quadratic algebras
Anatol N. Kirillov
We study some quadratic algebras which are appeared in the low-dimensional topology and Schubert calculus. We introduce the Jucys-Murphy elements in the braid algebra and in the pu…
Cauchy identities for universal Schubert polynomials
Anatol N. Kirillov
We prove the Cauchy type identities for the universal double Schubert polynomials, introduced recently by W. Fulton. As a corollary, the determinantal formulae for some specializat…
Quantum Schubert polynomials and quantum Schur functions
Anatol N. Kirillov
We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum…