1 7 Ja n 20 08 Classification of Harish - Chandra modules over the W - algebra W ( 2 , 2 ) ∗
نویسندگان
چکیده
In this paper, we classify all irreducible weight modules with finite dimensional weight spaces over the W -algebra W (2, 2). Meanwhile, all indecomposable modules with one dimensional weight spaces over the W -algebra W (2, 2) are also determined.
منابع مشابه
Ja n 20 08 Classification of Harish - Chandra modules over the W - algebra W ( 2 , 2 ) ∗
In this paper, we classify all irreducible weight modules with finite dimensional weight spaces over the W -algebra W (2, 2). Meanwhile, all indecomposable modules with one dimensional weight spaces over the W -algebra W (2, 2) are also determined.
متن کاملLie bialgebra structures on the W - algebra W ( 2 , 2 ) 1
Abstract. Verma modules over the W -algebra W (2, 2) were considered by Zhang and Dong, while the Harish-Chandra modules and irreducible weight modules over the same algebra were classified by Liu and Zhu etc. In the present paper we shall investigate the Lie bialgebra structures on the referred algebra, which are shown to be triangular coboundary.
متن کاملClassification of irreducible weight modules over W - algebra W ( 2 , 2 ) ∗
We show that the support of an irreducible weight module over the W -algebra W (2, 2), which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the the W -algebra W (2, 2), having a nontrivial finite dimensional weight spac...
متن کاملD ec 1 99 7 Matrix elements of vertex operators of deformed W - algebra and Harish Chandra Solutions to Macdonald ’ s difference equations
In this paper we prove that certain matrix elements of vertex operators of deformed W-algebra satisfy Macdonald difference equations and form n! -dimensional space of solutions. These solutions are the analogues of Harish Chandra solutions with prescribed asymptotic behavior. We obtain formulas for analytic continuation as a consequence of braiding properties of vertex operators of deformed W-a...
متن کاملGelfand - Kirillov Conjecture and Harish - Chandra Modules for Finite W - Algebras
We address two problems regarding the structure and representation theory of finite W -algebras associated with the general linear Lie algebras. Finite W -algebras can be defined either via the Whittaker modules of Kostant or, equivalently, by the quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of the finite W a...
متن کامل