The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra {\mathfrak{osp}(1|2n)} |
| |
Authors: | S Lievens N I Stoilov J Van der Jeugt |
| |
Institution: | (1) Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium;(2) Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria |
| |
Abstract: | It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the
present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters.
NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity
Attraction Poles Programme (Belgian State – Belgian Science Policy).
An erratum to this article can be found at |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|