9 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…
Scattering rules in soliton cellular automata associated with crystal bases
G. Hatayama, A. Kuniba, M. Okado +2
Solvable vertex models in a ferromagnetic regime give rise to soliton cellular automata at q=0. By means of the crystal base theory, we study a class of such automata associated wi…
Combinatorial R matrices for a family of crystals : C^{(1)}_n and A^{(2)}_{2n-1} cases
Goro Hatayama, Atsuo Kuniba, Masato Okado +1
The combinatorial R matrices are obtained for a family {B_l} of crystals for U'_q(C^{(1)}_n) and U'_q(A^{(2)}_{2n-1}), where B_l is the crystal of the irreducible module correspond…