Extension of the correspondence to the infinite-dimensional chiral spinors and self dual tensors

Abstract

The spinor representations of the orthosymplectic Lie superalgebras are considered and constructed. These are infinite-dimensional irreducible representations, of which the superdimension coincides with the dimension of the spinor representation of . Next, we consider the self dual tensor representations of and their generalizations: these are also infinite-dimensional and correspond to the highest irreducible component of the pth power of the spinor representation. We determine the character of these representations, and deduce a superdimension formula. From this, it follows that also for these representations the correspondence holds.