This paper summarizes the derivation of an explicit and global formula for the character of any holomorphic discrete series representation of a reductive Lie group G which satisfies certain conditions. The only very restrictive condition is that G/K be a Hermitian symmetric space. (Here K is the maximal compact subgroup of G.).

Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction o...

Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.

The phase space of theWess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group G is defined and the corresponding symplectic form is given. We present a careful derivation of the Poisson brackets of the Wess-Zumino-Witten model. We also study the canonical structure of the supersymmetric and the gauged Wess-Zumino-Witten models.

We study the Lie point symmetries and similarity transformations for partial differential equations of nonlinear one-dimensional magnetohydrodynamic system with Hall term known as HMHD system. For this 1+1 we find that is invariant under action a seventh dimensional algebra. Furthermore, optimal derived while invariants are applied derivation transformations. present different kinds oscillating...

We establish results about the second cohomology with coefficients in trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over commutative associative without unit. These provide simple unified approach to number questions treated earlier completely separated ways: periodization semisimple algebras (Anna Larsson), derivation algebras, prescribed part, ni...