Lie algebra representations of dimension $<p\sp 2$

Decomposing Lie Algebra Representations Using Crystal Graphs

We use the theory of crystal graphs to give a simple graph-theoretical algorithm for determining the branching rule for decomposing a representation of a simple Lie algebra when restricted to a simple subalgebra. We also describe a computer package for determining such decomposi-tions graphically. 0.1 Introduction When modeling elementary particle interactions and symmetry breaking in physics i...

String Junctions for Arbitrary Lie Algebra Representations

We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through invariant charges that count the effective number of prongs ending on each brane. Each equivalence class defines a point on a lattice of junctions. We define a me...

On Nambu-Lie 3-algebra representations

We propose a recipe to construct matrix representations of Nambu– Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.

Lie Representations and an Algebra Containing Solomon's

We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric grou...

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups