CONSTRUCTING IRREDUCIBLE REPRESENTATIONS OF QUANTUM GROUPS Uq(fm(K))
نویسنده
چکیده
In this paper, we construct families of irreducible representations for a class of quantum groups Uq(fm(K)). First, we give a natural construction of irreducible weight representations for Uq(fm(K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of Uq(fm(K)). As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.
منابع مشابه
On Representations of Quantum Groups
We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite dimensional weight representation of Uq(fm(K,H))...
متن کاملCONSTRUCTING IRREDUCIBLE REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K))
As generalizations of Uq(sl2), a class of algebras Uq(f(K)) were introduced and studied in [7]. For some special parameters f(K) = a(Km − K−m), a 6= 0, m ∈ N, Uq(f(K)) are Hopf algebras and hence quantum groups in the sense of Drinfeld ([3]). In this paper, we realize these algebras as Hyperbolic algebras ([12]). As an application of this realization, we obtain a natural construction of irreduc...
متن کاملON REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K,H))
An interesting class of algebras Uq(f(K, H)) were introduced and studied in [10] as further generalizations of another class of algebras Uq(f(K)) introduced in [11] (which are similar to Uq(sl2)). This new class of algebras include the Drinfeld double of the Borel subalgebra Uq(sl2) of the quantized enveloping algebra Uq(sl2) (or equivalently the two parameter quantum groups Ur,s(sl2) as studie...
متن کاملq-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...
متن کاملON REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K, H)) To Prof. Yingbo Zhang on the occasion of her 60th birthday
As further generalizations of Uq(sl2), an interesting class of algebras Uq(f(K,H)) was introduced and studied in [10]. In this paper, we further study these algebras by realizing them as Hyperbolic algebras. Such a realization yields a natural construction of interesting families of irreducible representations of Uq(f(K,H)) by using methods in non-commutative algebraic geometry([16]). We also i...
متن کامل