Weyl orbit-orbit branching rules for Lie algebras

• Main Author: Thoma, Martin.
• Other Authors: Sharp, R. T. (advisor)
• Format: Others
• Language: en
• Published: McGill University 1997
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=35416

This thesis is devoted to branching rules for Lie algebras, that is the description of decompositions of algebra representations upon restriction to a subalgebra, and consists of three major parts. === In the first part the Weyl orbit-orbit branching rules are calculated for all classical simple Lie algebra - maximal regular reductive subalgebra pairs: Cm+n⊃Cm⊕C n, Dm+n⊃Dm⊕D n, Bm+n⊃Dm⊕B n, Am+n+1⊃Am⊕An⊕ u1, Bm+1⊃Bm⊕u1 , Cm+1⊃Am⊕u1 , Dm+1⊃Dm⊕u1 , Dm+1⊃Am⊕u1 . The branching rules are given in terms of integrity bases and compatibility rules. === In the second part we use results from the first part to derive the complete branching rules (i.e. representation-representation branching rules) for the algebra subalgebra series son ⊃son-2 ⊕u1. The branching rules are given in terms of generating functions. === The third part is in character similar to the first part---the Weyl orbit-orbit branching rules are computed for affine algebra-subalgebra, pairs obtained from the pairs listed above by affinization. The rules are presented in terms of integrity bases and compatibility rules.