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On crystal bases of the $Q$-analogue of universal enveloping algebras
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
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
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
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
Geometric construction of crystal bases
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
On the Segal-Shale-Weil representations and harmonic polynomials
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