8 citations · 13 across the 3 of their papers we have counts for
15 papers
On the X=M=K Conjecture
Mark Shimozono
In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship wit…
Deformed universal characters for classical and affine algebras
Mark Shimozono, Mike Zabrocki
Creation operators are given for the three distinguished bases of the type BCD universal character ring of Koike and Terada yielding an elegant way of treating computations for all…
Four positive formulae for type A quiver polynomials
Allen Knutson, Ezra Miller, Mark Shimozono
We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton. All four formulae are combinatorial, in the sense that they are expressed in ter…
A crystal to rigged configuration bijection for nonexceptional affine algebras
Masato Okado, Anne Schilling, Mark Shimozono
Kerov, Kirillov, and Reshetikhin defined a bijection between highest weight vectors in the crystal graph of a tensor power of the vector representation, and combinatorial objects c…
A Tensor Product Theorem Related To Perfect Crystals
Masato Okado, Anne Schilling, Mark Shimozono
Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect…
Virtual crystals and fermionic formulas of type , , and
Masato Okado, Anne Schilling, Mark Shimozono
We introduce ``virtual'' crystals of the affine types , and by naturally extending embeddings of crystals of types and into…