n -representation infinite algebras

Structure and Representation Theory of Infinite-dimensional Lie Algebras

Kac-Moody algebras are a generalization of the finite-dimensional semisimple Lie algebras that have many characteristics similar to the finite-dimensional ones. These possibly infinite-dimensional Lie algebras have found applications everywhere from modular forms to conformal field theory in physics. In this thesis we give two main results of the theory of Kac-Moody algebras. First, we present ...

Infinite-dimensional Lie algebras

Infinite product representation of solution of indefinite SturmLiouville problem

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

Lie algebras , their representation theory and GL n Minor

5 The special linear Lie algebra sl(n,C) and the general linear group GLn(C) 22 5.1 Structure of sl(n,C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Representations of sl(n,C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Weyl’s construction, tensor products and some combinatorics . . . . . . . . . . . . . . . . ....

Structure Constants for New Infinite-Dimensional Lie Algebras of U(N+, N−) Tensor Operators and Applications

The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U(N+, N−) are provided. They generalize the Virasoro and W∞ algebras to higher dimensions. The connection with volumepreserving diffeomorphisms on M , higher generalized-spin and tensor operator algebras of U(N+, N−) is discussed. These centrally-extended, infinite-...