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 ...

We study the resonances of Laplacian acting on compactly supported sections a homogeneous vector bundle over Riemannian symmetric space non-compact type. The is assumed to have rank-one but irreducible representation ? K defining arbitrary. determine resonances. Under additional assumption that occurs in spherical principal series, we resonance representations. They are all irreducible. find th...

We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree. This is used to prove our main theorem: An algebra is of finite representation type if and only if for every indecomposable projective the inclusion of the ...

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))...

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...

The Lie algebra D̂, which is the unique non-trivial central extension of the Lie algebra D of differential operators on the circle [KP1], has appeared recently in various models of two-dimensional quantum field theory and integrable systems, cf., e.g., [BK, FKN, PRS, IKS, CTZ, ASvM]. A systematic study of representation theory of the Lie algebra D̂, which is often referred to as W1+∞ algebra, was...

We give a polynomial basis of each irreducible representation of the Hecke algebra, as well as an adjoint basis. Decompositions in these bases are obtained by mere specializations.

We construct 2-functors from a 2-category categorifying quantum sl n to 2-categories categorifying the irreducible representation of highest weight 2ω k .

We construct 2-functors from a 2-category categorifying quantum sl(n) to 2-categories categorifying the irreducible representation of highest weight 2ωk.