ar X iv : q - a lg / 9 60 70 31 v 1 3 0 Ju l 1 99 6 Level - 0 action of U q ( ŝl n ) on the q - deformed Fock spaces

ar X iv : q - a lg / 9 60 70 28 v 1 2 7 Ju l 1 99 6 Examples of Categorification

ar X iv : 0 90 2 . 10 22 v 1 [ nl in . S I ] 6 F eb 2 00 9 Wakimoto realization of the elliptic algebra U q , p ( ŝl N )

We construct a free field realization of the elliptic quantum algebra Uq,p(ŝlN ) for arbitrary level k 6= 0,−N . We study Drinfeld current and the screening current associated with Uq,p(ŝlN ) for arbitrary level k. In the limit p → 0 this realization becomes q-Wakimoto realization for Uq(ŝlN ).

ar X iv : q - a lg / 9 70 60 09 v 1 1 1 Ju n 19 97 q - Deformation of the Krichever - Novikov Algebra

Using q-operator product expansions between U (1) current fields and also the corresponding energy-momentum tensors, we furnish the q-analoques of the generalized Heisenberg algebra and the Krichever-Novikov algebra.

ar X iv : q - a lg / 9 70 70 31 v 1 2 4 Ju l 1 99 7 DOUBLE QUANTIZATION ON THE COADJOINT REPRESENTATION OF

For g = sl(n) we construct a two parametric U h (g)-invariant family of algebras, (Sg) t,h , that is a quantization of the function algebra Sg on the coadjoint representation. Along the parameter t the family gives a quantiza-tion of the Lie bracket. This family induces a two parametric U h (g)-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-S...

Level - 0 action of U q ( c sl n ) on the q - deformed Fock spaces

On the level-1 Fock space modules of the algebra U q ( b sl n ) we de ne a level-0 action U 0 of the U 0 q ( b sl n ), and an action of an Abelian algebra of conserved Hamiltonians commuting with the U 0 . An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials. 1 e-...