1 citations · 1 across the 5 of their papers we have counts for
8 papers
Geometric Crystals on Unipotent Groups and Generalized Young Tableaux
Toshiki Nakashima
We define geometric/unipotent crystal structure on unipotent subgroups of semi-simple algebraic groups. We shall show that in -case, their ultra-discretizations coincide with…
Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Type A
Ayumu Hoshino, Toshiki Nakashima
We describe the crystal bases of modified quantum algebras and its connected component containing ``zero vector''by the polyhedral realization method for the types A_n and A^(1)_1.…
Geometric Crystals on Schubert Varieties
Toshiki Nakashima
We define geometric crystals and unipotent crystals for arbitrary Kac-Moody groups and describe geometric and unipotent crystal structures on the Schubert varieties.
Extremal Projectors of q-Boson Algebras
Toshiki Nakashima
We define the extremal projector of the -boson Kashiwara algebra and study their basic properties. Applying their proerties to the representation theory of the catego…
On certain maximal cyclic modules for the quantized special linear algebra at a root of unity
Masaharu Kaneda, Toshiki Nakashima
By properly specializing the parameters irreducible modules of maximal dimension for the De Concini-Kac version of the Drinfeld-Jimbo quantum algebra in type may be transformed…
Polytopes for Crystallized Demazure Modules and Exremal Vectors
Toshiki Nakashima
We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions…