Translation for Finite W -algebras
نویسنده
چکیده
A finite W -algebra U(g, e) is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element e of a complex reductive Lie algebra g. It is possible to give the tensor product of a U(g, e)-module with a finite dimensional U(g)module the structure of a U(g, e)-module; we refer to such tensor products as translations. In this paper, we present a number of fundamental properties of these translations, which are expected to be of importance in understanding the representation theory of U(g, e).
منابع مشابه
Translation invariant surfaces in the 3-dimensional Heisenberg group
In this paper, we study translation invariant surfaces in the 3-dimensional Heisenberg group $rm Nil_3$. In particular, we completely classify translation invariant surfaces in $rm Nil_3$ whose position vector $x$ satisfies the equation $Delta x = Ax$, where $Delta$ is the Laplacian operator of the surface and $A$ is a $3 times 3$-real matrix.
متن کامل1 9 A ug 2 00 9 TRANSLATION FOR FINITE W - ALGEBRAS
A finite W-algebra U (g, e) is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element e of a complex reductive Lie algebra g. It is possible to give the tensor product of a U (g, e)-module with a finite dimensional U (g)-module the structure of a U (g, e)-module; we refer to such tensor products as trans...
متن کاملFinite Dimensional Representations of W -algebras
W -algebras of finite type are certain finitely generated associative algebras closely related to universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete classification of finite dimensional irreducible modules for W -algebras. Also we get some partial results towards a conjecture by Ginzburg on their finite dimension...
متن کاملINITIAL RAMIFICATION INDEX OF NONINVARIANT VALUATIONS ON FINITE DIMENSIONAL DIVISION ALGEBRAS
Let D be a division ring with centre K and dim, D< ? a valuation on K and v a noninvariant extension of ? to D. We define the initial ramfication index of v over ?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation rings A , A ,…, A . If B= A , it is shown that the following conditions are equivalent: (i) B i...
متن کاملSmarandache algebras and their subgroups
In this paper we define S algebras and show that every finite group can be found in some S algebra. We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.
متن کاملWeighted Convolution Measure Algebras Characterized by Convolution Algebras
The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.
متن کامل