Rogers-Ramanujan type partition identities establish equalities between certain types of partitions with difference conditions and partitions whose generating functions is an infinite product. Since the 1980’s, many connections between representations of Lie algebras and RogersRamanujan type partition identities have emerged. Lepowsky and Wilson [6] were the first to establish this link by givi...

We construct and study various dual pairs between finite dimensional classical Lie groups and infinite dimensional Lie algebras in some Fock representations. The infinite dimensional Lie algebras here can be either a completed infinite rank affine Lie algebra, the W1+∞ algebra or its certain Lie subalgebras. We give a formulation in the framework of vertex algebras. We also formulate several co...

Bundles of C*-algebras can be used to represent limits physical theories whose algebraic structure depends on the value a parameter. The primary example is [Formula: see text] limit quantities in quantum theories, represented framework strict deformation quantization. In this paper, we understand such limiting procedures terms extension bundle some We prove existence and uniqueness results for ...

We discuss the mutually opposite procedures of deformations and contractions of Lie algebras. Our main purpose is to illustrate the fact that, with appropriate combinations of both procedures, we obtain new Lie algebras. Firstly, we discuss low-dimensional Lie algebras, and these simple examples illustrate that, whereas for every contraction there exists a reverse deformation, the converse is n...

Orthogonal decompositions (OD:s) that are monomial have been constructed for most simple Lie algebras but in some cases the existence of an OD is still an open question. One of them is Lie algebras of type Cn where n is not a power of 2. In this paper we use computational methods to prove that C3 has no monomial OD. 1 Orthogonal decompositions of simple Lie algebras The basic question, of which...

In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is ...

Introduction 1 1. Preliminaries 6 2. Generic stabilisers (centralisers) for the adjoint representation 9 3. Generic stabilisers for the coadjoint representation 10 4. Semi-direct products of Lie algebras and modules of covariants 12 5. Generic stabilisers and rational invariants for semi-direct products 14 6. Reductive semi-direct products and their polynomial invariants 21 7. Takiff Lie algebr...