8 citations · 13 across the 3 of their papers we have counts for
11 papers · 1 filter
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…
Crystal bases and q-identities
Masato Okado, Anne Schilling, Mark Shimozono
The relation of crystal bases with -identities is discussed, and some new results on crystals and -identities associated with the affine Lie algebra are presented…
Hall-Littlewood vertex operators and generalized Kostka polynomials
Mark Shimozono, Mike Zabrocki
A family of vertex operators that generalizes those given by Jing for the Hall-Littlewood symmetric functions is presented. These operators produce symmetric functions related to t…
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…