Invariant integration on orthosymplectic and unitary supergroups
- Author
- Kevin Coulembier (UGent) and Zhang Ruibin
- Organization
- Abstract
- The orthosymplectic supergroup OSp(m|2n) and unitary supergroup U(p|q) are studied following a new approach that starts from Harish-Chandra pairs and links the sheaf-theoretical supermanifold approach of Berezin and others with the differential geometry approach of Rogers and others. Thematrix elements of the fundamental representation of the Lie supergroup G are expressed in terms of functions on the product supermanifold G(0)circle times R-0|N, with G(0) the underlying Lie group and N the odd dimension of G. This product supermanifold is isomorphic to the supermanifold of G. This leads to a new expression for the standard generators of the corresponding Lie superalgebra g as invariant derivations on G. Using these results, a new and transparent formula for the invariant integrals on OSp(m|2n) and U(p|q) is obtained.
- Keywords
- ALGEBRAS, SUPERSYMMETRY, REPRESENTATIONS, LIE SUPERGROUPS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-2067039
- MLA
- Coulembier, Kevin, and Zhang Ruibin. “Invariant Integration on Orthosymplectic and Unitary Supergroups.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 45, no. 9, 2012, doi:10.1088/1751-8113/45/9/095204.
- APA
- Coulembier, K., & Ruibin, Z. (2012). Invariant integration on orthosymplectic and unitary supergroups. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(9). https://doi.org/10.1088/1751-8113/45/9/095204
- Chicago author-date
- Coulembier, Kevin, and Zhang Ruibin. 2012. “Invariant Integration on Orthosymplectic and Unitary Supergroups.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45 (9). https://doi.org/10.1088/1751-8113/45/9/095204.
- Chicago author-date (all authors)
- Coulembier, Kevin, and Zhang Ruibin. 2012. “Invariant Integration on Orthosymplectic and Unitary Supergroups.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45 (9). doi:10.1088/1751-8113/45/9/095204.
- Vancouver
- 1.Coulembier K, Ruibin Z. Invariant integration on orthosymplectic and unitary supergroups. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2012;45(9).
- IEEE
- [1]K. Coulembier and Z. Ruibin, “Invariant integration on orthosymplectic and unitary supergroups,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 45, no. 9, 2012.
@article{2067039,
abstract = {{The orthosymplectic supergroup OSp(m|2n) and unitary supergroup U(p|q) are studied following a new approach that starts from Harish-Chandra pairs and links the sheaf-theoretical supermanifold approach of Berezin and others with the differential geometry approach of Rogers and others. Thematrix elements of the fundamental representation of the Lie supergroup G are expressed in terms of functions on the product supermanifold G(0)circle times R-0|N, with G(0) the underlying Lie group and N the odd dimension of G. This product supermanifold is isomorphic to the supermanifold of G. This leads to a new expression for the standard generators of the corresponding Lie superalgebra g as invariant derivations on G. Using these results, a new and transparent formula for the invariant integrals on OSp(m|2n) and U(p|q) is obtained.}},
articleno = {{095204}},
author = {{Coulembier, Kevin and Ruibin, Zhang}},
issn = {{1751-8113}},
journal = {{JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}},
keywords = {{ALGEBRAS,SUPERSYMMETRY,REPRESENTATIONS,LIE SUPERGROUPS}},
language = {{eng}},
number = {{9}},
pages = {{35}},
title = {{Invariant integration on orthosymplectic and unitary supergroups}},
url = {{http://doi.org/10.1088/1751-8113/45/9/095204}},
volume = {{45}},
year = {{2012}},
}
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