THE WEYL CHARACTER FORMULA, THE HALF-SPIN REPRESENTATIONS, AND EQUAL RANK SUBGROUPS

Let B be a reductive Lie subalgebra of a semi-simple Lie algebra F of the same rank both over the complex numbers. To each finite dimensiona l irreducible representation V-lambda, of F we assign a multiplet of i rreducible representations of B with m elements in each multiplet, whe re m is the index of the Weyl group of B in the Weyl group of F, We ob tain a generalization of the Weyl character formula; our formula gives the character of V-lambda as a quotient whose numerator is an alterna ting sum of the characters in the multiplet associated to V-lambda and whose denominator is an alternating sum of the characters of the mult iplet associated to the trivial representation of F.