Constructing irreducible representations of discrete groups
نویسندگان
چکیده
منابع مشابه
CONSTRUCTING 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 کاملCONSTRUCTING IRREDUCIBLE REPRESENTATIONS OF QUANTUM GROUPS Uq(fm(K))
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 ...
متن کاملComputing Irreducible Representations of Groups
How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers ; and there remain practical difficulties even for groups of relatively small orders ( á 100). The present ...
متن کاملIrreducible Representations of Diperiodic Groups
The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a generalized translational group and an axial point group. The results are presented in the form of the tables, containing the matrices of the irreducible represent...
متن کاملConstructing Irreducible Representations of Finitely Presented Algebras
We describe an algorithmic test, using the “standard polynomial identity” (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When ndimensional irreducible representations do exist, our proposed procedure can (in principle) produce explicit constructions.
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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 1997
ISSN: 0253-4142,0973-7685
DOI: 10.1007/bf02867253