Representations of the generalized Lie algebra

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups

2 0 M ar 1 99 8 Representations of the Generalized Lie Algebra sl ( 2 ) q

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra sl(2) q introduced by Lyubashenko and the second named author. We consider separately the cases of q generic and q at roots of unity. Some of the representations have no classical analog even for generic q. Some of the representations have no analog to the finite-dimensiona...

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.