A class of infinite-dimensional representations of the Lie superalgebra \mathfrak{o}\mathfrak{s}\mathfrak{p}(2m+1|2n) and the parastatistics Fock space
Abstract
An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a lowest weight of the form ≤ft[ -\frac{p}{2},\ldots ,-\frac{p}{2}|\frac{p}{2},\ldots ,\frac{p}{2} \right], p being a positive integer. Explicit expressions for the transformation of the basis under the action of algebra generators are found. Since the relations of algebra generators correspond to the defining relations of m pairs of parafermion operators and n pairs of paraboson operators with relative parafermion relations, the parastatistics Fock space of order p is also explicitly constructed. Furthermore, the representations V(p) are shown to have interesting characters in terms of supersymmetric Schur functions, and a simple character formula is also obtained.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- April 2015
- DOI:
- 10.1088/1751-8113/48/15/155202
- arXiv:
- arXiv:1502.07656
- Bibcode:
- 2015JPhA...48o5202S
- Keywords:
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- Mathematical Physics;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 15 pages