Applications of S-function techniques to the representation theory of Lie superalgebras and symmetry breaking

Cummins, Christopher John (1986) Applications of S-function techniques to the representation theory of Lie superalgebras and symmetry breaking. University of Southampton, Doctoral Thesis.

Abstract

The theory of Schur or S-functions and its applications to the character theory of the classical Lie groups and Lie algebras is reviewed. New identities involving infinite S-function series are presented which lead to a new proof of the Newell-Littlewood formula for the products of orthogonal and symplectic characters. The character theory of Lie superalgebras is surveyed, and supercharacters associated with Young diagrams are defined for Osp(M/N) and U(M/N). Modification rules for these characters are derived and discussed, in the othosymplectic case their relationship with Kac's character formula for typical representations is made explicit. Finally symmetry breaking patterns in unified gauge field theories are studied with the aid of S-function methods. By developing the theory of canonical forms of tensor representations several new examples of symmetry breaking patterns are found in the case of third rank antisymmetric tensor representation. With the aid of a technique due to J.S. Kim a more complicated example involving the seventy five dimensional representation of SU(5) is analysed, and a counter-example to an important conjecture of Michel is obtained. (D73014/87)

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