Extension of the osp(m|n)~ so(m-n) Correspondence to the Infinite-Dimensional Chiral Spinors and Self Dual Tensors

Abstract

The spinor representations of the orthosymplectic Lie superalgebras osp(m|n) are considered and constructed. These are infinite-dimensional irreducible representations, of which the superdimension coincides with the dimension of the spinor representation of so(m-n). Next, we consider the self dual tensor representations of osp(m|n) and their generalizations: these are also infinite-dimensional and correspond to the highest irreducible component of the $p^{th}$ 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 osp(m|n)~ so(m-n) correspondence holds.

References in corpus (4)

• The parafermion Fock space and explicit so(2n+1) representations
• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space
• Representations of affine superalgebras and mock theta functions III
• Reduced matrix elements of the orthosymplectic Lie superalgebra

Cited by in corpus (2)

• Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks
• On characters and superdimensions of some infinite-dimensional irreducible representations of $\mathfrak{osp}(m|n)$