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On crystal bases of the $Q$-analogue of universal enveloping algebras
- M. Kashiwara
- Mathematics
- 1 July 1991
0. Introduction. The notion of the q-analogue of universal enveloping algebras is introduced independently by V. G. Drinfeld and M. Jimbo in 1985 in their study of exactly solvable models in the…
TRANSFORMATION GROUPS FOR SOLITON EQUATIONS
- E. Date, M. Kashiwara, T. Miwa, M. Jimbo
- Materials Science
- 1982
A printing blanket and method of making same is provided wherein such blanket comprises a base structure, a surface layer made of a fluorocarbon elastomer, and a binder layer comprised of a…
Crystalizing theq-analogue of universal enveloping algebras
- M. Kashiwara
- Mathematics
- 1 October 1990
For an irreducible representation of theq-analogue of a universal enveloping algebra, one can find a canonical base atq=0, named crystal base (conjectured in a general case and proven forAn, Bn, Cn…
Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras
- M. Kashiwara, Toshiki Nakashima
- Mathematics
- 15 April 1994
The explicit form of the crystal graphs for the finite-dimensional representations of the q-analogue of the universal enveloping algebras of type A, B, C, and D is given in terms of semi-standard…
The crystal base and Littelmann’s refined Demazure character formula
- M. Kashiwara
- Mathematics
- 1 September 1993
Geometric construction of crystal bases
- M. Kashiwara, Yoshihisa Saito
- Mathematics
- 8 June 1996
We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As…
Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type
- E. Date, M. Jimbo, M. Kashiwara, T. Miwa
- Mathematics
- 1 March 1982
On the Segal-Shale-Weil representations and harmonic polynomials
- M. Kashiwara, M. Vergne
- Mathematics
- 1 February 1978
In this paper, we give the answer to the following two intimately related problems. (a) To decompose the tensor products of the harmonic representations into irreducible components to get a series of…
Crystal bases of modified quantized enveloping algebra
- M. Kashiwara
- Mathematics
- 1 February 1994
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