Let G be a connected reductive linear algebraic group over C and let (; V) be a regular representation of G. There is a locally-nite representation (^ ; C V ]) on the aane algebra C V ] of V deened by ^ (g)f(v) = f(g ?1 v) for f 2 C V ]. Since G is reductive, (^ ; C V ]) decomposes as a direct sum of irreducible regular representations of G. The representation (; V) is said to be multiplicity f...

This article concerns commutative factor rings for ideals contained in the center. A ring $R$ is called CIFC if $R/I$ some proper ideal $I$ of with $I\subseteq Z(R)$, where $Z(R)$ center $R$. We prove that (i) a $R$, $W(R)$ contains all nilpotent elements (hence Köthe's conjecture holds $R$) and $R/W(R)$ reduced ring; (ii) strongly bounded $R/N_*(R)$ $0\neq N_*(R)\subseteq (resp., $N_*(R)$) Wed...

We study the representation theory of the W -algebra Wk(ḡ) associated with a simple Lie algebra ḡ at level k. We show that the “−” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k ∈ C. Moreover, we show that the character of each irreducible highest weight representation of Wk(ḡ) is completely determined by that of the corresponding irre...

The W3 algebra of central charge 6/5 is realized as a subalgebra of the vertex operator algebra V2A2 associated with a lattice of type √ 2A2 by using both coset construction and orbifold theory. It is proved that W3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.

Starting from a Hecke R−matrix, Jing and Zhang constructed a new deformation Uq(sl2) of U(sl2), and studied its finite dimensional representations in [6]. Especically, this algebra is proved to be just a bialgebra, and all finite dimensional irreducible representations are constructed in [6]. In addition, an example is given to show that not every finite dimensional representation of this algeb...

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

By assuming the parameter q ∈ C∗ is not a root of unity and introducing the notion of standard Kleshchev multipartitions, we establish a one-to-one correspondence between standard Kleshchev multipartitions and irreducible representations with integral weights of the affine Hecke algebra of type A. Then, on the one hand, we extend the correspondence to all Kleshchev multipartitions for a given A...

In this paper the W -algebra W (2, 2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible W (2, 2)-module or a tensor product of two irreducible Virasoro vertex operator algebras. Furthermore, any rational, C2-cofinite and simple vertex operator alg...

We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the Lie algebra of vector fields. We prove this result by studying vertex algebras associated with the Lie algebra of ve...