On the Lie superalgebra embedding C(n+1)⊃B(0,n) and dimension formulas: On the Lie superalgebra embedding \(C(n+1)\supset B(0,n)\) and dimension formulas
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| Title: | On the Lie superalgebra embedding C(n+1)⊃B(0,n) and dimension formulas: On the Lie superalgebra embedding \(C(n+1)\supset B(0,n)\) and dimension formulas |
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| Authors: | J. Van der Jeugt |
| Source: | Journal of Mathematical Physics. 37:4176-4186 |
| Publisher Information: | AIP Publishing, 1996. |
| Publication Year: | 1996 |
| Subject Terms: | Superalgebras, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), superdimension formulas, dimension formulas, 0103 physical sciences, typical representations, orthosymplectic Lie superalgebras \(\text{osp} (m/2n)\), 0101 mathematics, 01 natural sciences, paraboson operators, branching rules, atypical irreducible representations |
| Description: | It is shown that the orthosymplectic Lie superalgebras osp (m/2n) have a nonregular subalgebra osp(1/2n). This implies that paraboson operators can be realized as elements of osp(m/2n). The embedding osp(2/2n)⊇osp(1/2n), or, in a different notation, C(n+1)⊇B(0,n), is studied in more detail. In particular, branching rules are determined for all typical and atypical irreducible representations of osp(2/2n) with respect to the subalgebra osp(1/2n). Finally, dimension and superdimension formulas are given for the Lie superalgebras under consideration. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.531696 |
| Access URL: | https://biblio.ugent.be/publication/189479 https://scitation.aip.org/content/aip/journal/jmp/37/8/10.1063/1.531696 http://ui.adsabs.harvard.edu/abs/1996JMP....37.4176V/abstract https://aip.scitation.org/doi/abs/10.1063/1.531696 |
| Accession Number: | edsair.doi.dedup.....a79bee4261fdfb28ad4b3b98417f6de5 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | It is shown that the orthosymplectic Lie superalgebras osp (m/2n) have a nonregular subalgebra osp(1/2n). This implies that paraboson operators can be realized as elements of osp(m/2n). The embedding osp(2/2n)⊇osp(1/2n), or, in a different notation, C(n+1)⊇B(0,n), is studied in more detail. In particular, branching rules are determined for all typical and atypical irreducible representations of osp(2/2n) with respect to the subalgebra osp(1/2n). Finally, dimension and superdimension formulas are given for the Lie superalgebras under consideration. |
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| ISSN: | 10897658 00222488 |
| DOI: | 10.1063/1.531696 |