N ov 2 00 3 Some deformations of U [ sl ( 2 ) ] and their representations

3 Some deformations of U [ sl ( 2 ) ] and their representations

Some one-and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite-dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters.

1 5 N ov 2 00 2 Representations of SL 2 and the distribution of points in

N ov 2 00 6 Categorification of level two representations of quantum sl n via generalized arc rings

Representation Theory of a Class of Hopf Algebras

The representations of the pointed Hopf algebras U and u are described, where U and u can be regarded as deformations of the usual quantized enveloping algebras Uq(sl(3)) and the small quantum groups respectively. It is illustrated that these representations have a close connection with those of the quantized enveloping algebras Uq(sl(2)) and those of the half quantum groups of sl(3).

SL(2;R)/U(1) Supercoset and Elliptic Genera of Non-compact Calabi-Yau Manifolds

We first discuss the relationship between the SL(2;R)/U(1) supercoset and N = 2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;R)/U(1) theory correspond exactly to those massless representations of N = 2 Liouville theory which are closed under modular transformations and studied in our previous wo...