Related papers: Generalized Casimir Operators
In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product…
There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…
A new class of operators, larger than $C$-symmetric operators and different than normal one, named $C$--normal operators is introduced. Basic properties are given. Characterizations of this operators in finite dimensional spaces using a…
The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive…
We study some non-highest weight modules over an affine Kac-Moody algebra at non-critical level. Roughly speaking, these modules are non-commutative localizations of some non-highest weight "vacuum" modules. Using free field realization, we…
We describe the generalized Casimir operators and their actions on the positive representations $P_{\lambda}$ of the modular double of split real quantum groups $U_{q\tilde{q}}(g_R)$. We introduce the notion of virtual highest and lowest…
We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients…
A full set of Casimir operators for the Lie superalgebra $gl(m/\infty)$ is constructed and shown to be well defined in the category $O_{FS}$ generated by the highest weight irreducible representations with only a finite number of non-zero…
We discuss the higher dimensional generalizations of the Virasoro and Affine Kac-Moody Lie algebras. We present an explicit construction for a central extensions of the Lie Algebra $Map (X, \g)$ where $\g$ is a finite-dimensional Lie…
In previous work, we introduced an algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. In this article we build on this work by applying the algorithm to several classes of finite…
Casimir operators -- the generators of the center of the enveloping algebra -- are described for simple or close to them ``classical'' finite dimensional Lie superalgebras with nondegenerate symmetric even bilinear form in Sergeev A., The…
The second order casimirs for the affine Krichever--Novikov algebras $\hat{\mathfrak{gl}}_{g,2}$ and $\hat{\mathfrak{sl}}_{g,2}$ are described. More general operators which we call semi-casimirs are introduced. It is proven that the…
The full set of Casimir elements of the centrally extended l-conformal Galilei algebra is found in simple and tractable form.
We give a full set of Casimir operators for the symplectic group of arbitrary genus in terms of a basis chosen such that the action on representations of known $K$-type becomes transparent. We give examples for the latter.
We show how to obtain from highest weight representations of Krichever-Novikov algebras of affine type (also called higher genus affine Kac-Moody algebras) representations of centrally extended Krichever-Novikov vector field algebras via…
Let V be a unitary space. Suppose G is a subgroup of the full symmetric group S_m and X is an irreducible unitary representation of G. In this paper, we introduce the generalized Cartesian symmetry class over V associated with G and X. Then…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities, for all simple Lie algebras we derive explicit formulae…
The standard Laplace operator is a generalization of the Hodge Laplace operator on differential forms to arbitrary geometric vector bundles, alternatively it can be seen as generalization of the Casimir operator acting on sections of…
In this paper we consider shift operators, self-adjoint, unitary and normal operators on the standard module over a unital C*-algebra A. We define various generalized spectra in A of these operators, give description of such spectra of…