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

TL;DR

This paper extends the known correspondence between osp(m|n) superalgebras and so(m-n) Lie algebras to include infinite-dimensional chiral spinors and self-dual tensors, providing new character formulas and superdimension relations.

Contribution

It introduces the infinite-dimensional spinor and self-dual tensor representations of osp(m|n) and establishes their correspondence with so(m-n), expanding the algebraic framework.

Findings

Constructed infinite-dimensional spinor representations with superdimension matching so(m-n)

Derived character formulas for self-dual tensor representations

Confirmed the osp(m|n)~ so(m-n) correspondence for these representations

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.