68 citations · 670 across the 62 of their papers we have counts for
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Bosonic formula for level-restricted paths
Anne Schilling, Mark Shimozono
We prove a bosonic formula for the generating function of level-restricted paths for the infinite families of affine Kac-Moody algebras. In affine type A this yields an expression…
Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties
Mark Shimozono
Answering a question of Kuniba, Misra, Okado, Takagi, and Uchiyama, it is shown that certain Demazure characters of affine type A, coincide with the graded characters of coordinate…
Multi-atoms and monotonicity of generalized Kostka polynomials
Mark Shimozono
The generalized Kostka polynomials are the Poincare polynomials of isotypic components of certain graded GL(n)-modules. The former satisfy a monotonicity property arising from natu…
A cyclage poset structure for Littlewood-Richardson tableaux
Mark Shimozono
A graded poset structure is defined for the sets of Littlewood-Richardson (LR) tableaux that count the multiplicity of an irreducible GL(n)-module in the tensor product of irreduci…
Graded characters of modules supported in the closure of a nilpotent conjugacy class
Mark Shimozono, Jerzy Weyman
We study the Poincare polynomials of isotypic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials gene…
A generalization of the Kostka-Foulkes polynomials
Anatol N. Kirillov, Mark Shimozono
Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-K…