Role of the orthogonal group in construction of osp(1|2n) representations

TL;DR

This paper explores how the orthogonal group influences the construction of osp(1|2n) representations, paralleling the symmetric group's role in unitary group representations, and addresses the reducibility of Green's ansatz representations.

Contribution

It demonstrates the orthogonal group's role in osp(1|2n) representations and solves the longstanding problem of reducibility in Green's ansatz representations.

Findings

Orthogonal group plays a key role in osp(1|2n) representations

Addresses reducibility of Green's ansatz representations

Provides a new framework for positive energy representations

Abstract

It is well known that the symmetric group has an important role (via Young tableaux formalism) both in labelling of the representations of the unitary group and in construction of the corresponding basis vectors (in the tensor product of the defining representations). We show that orthogonal group has a very similar role in the context of positive energy representations of osp(1|2n,R). In the language of parabose algebra, we essentially solve the long standing problem of reducibility of Green's ansatz representations.