ON REPRESENTATIONS OF QUANTUM GROUPS U_q(f_m(K,H))

Abstract

We construct families of irreducible representations for a class of quantum groups U q ( f m (K , H ). First, we realize these quantum groups as hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for U q ( f m (K , H )). Second, we study the relationship between U q ( f m (K , H )) and U q ( f m (K )). As a result, any finite-dimensional weight representation of U q ( f m (K , H )) is proved to be completely reducible. Finally, we study the Whittaker model for the center of U q ( f m (K , H )), and a classification of all irreducible Whittaker representations of U q ( f m (K , H )) is obtained.2000 Mathematics subject classification: 17B10, 17B35, 17B37.

Hopf structures on ambiskew polynomial rings

“…In this section we will extend the Hopf structure on R to A. We make the following anzats, guided by [4] and [6]:…”

“…The quantum group U q (sl 2 (C)) has by definition the structure of a Hopf algebra. In [6], an extension of this quantum group to an associative algebra denoted by U q (f (H, K)) (where f is a Laurent polynomial in two variables) is defined and finite-dimensional representations are studied. The authors show that under certain conditions on f , a Hopf algebra structure can be introduced.…”

Single event transient propagation in dynamic complementary metal oxide semiconductor cascade circuits

“…In large-scale combinational logic circuits, dynamic complementary metal oxide semiconductor (CMOS) circuits are widely used in high-speed integrated circuits due to their smaller area and faster speed [4,5,6]. At present, there are some studies on the SET generation mechanism in single dynamic CMOS logic.…”

Augmented down-up algebras and uniform posets

“…However, it appears that the down-up algebra concept is not sufficiently robust to handle Polar b (N, ǫ) or A b (N, M). The same can be said for the generalized down-up algebras [8] and all the related algebras [1,2,4,7,[9][10][11][12][13][15][16][17][19][20][21][22][25][26][27] that we are aware of. In the present paper we introduce a family of algebras called augmented down-up algebras, or ADU algebras for short.…”