Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-04-23
Commun.Math.Phys. 143 (1991) 1-16
Physics
High Energy Physics
High Energy Physics - Theory
22 pp
Scientific paper
The signatures of the inner product matrices on a Lie algebra's highest weight representation are encoded in the representation's signature character. We show that the signature characters of a finite-dimensional Lie algebra's highest weight representations obey simple difference equations that have a unique solution once appropriate boundary conditions are imposed. We use these results to derive the signature characters of all $A_2$ and $B_2$ highest weight representations. Our results extend, and explain, signature patterns analogous to those observed by Friedan, Qiu and Shenker in the Virasoro algebra's representation theory.
Kent Adrian
Watts Galen
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