Mathematical Sciences

Lund University

  • Title: Tensor Product Decomposition in Lie Algebra Representation Theory
  • Description: The basic theory of semisimple Lie algebras and their representations is studied in detail. In particular it is shown that every irreducible module V (λ) is uniquely determined up to isomorphism by its highest weight λ. Then the problem of decomposing a tensor product of two finite dimensional modules into a direct sum of irreducible modules is considered. It is shown that for λ fixed, the decompositions of V (λ) V (μ) for a finite set of μ’s are sufficient to obtain all such decompositions. Some decomposition formulas are given, in particular a geometric method is presented along with several examples.
  • Start Date: Feb. 4, 2011
  • Finished Date: Feb. 4, 2011
  • Supervisor: Arne Meurman
  • Student: Jonathan Nilsson
  • Report (553.7 KB)
  • Popular Science Report (11.8 KB)