Invariant integration on orthosymplectic and unitary supergroups
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. The matrix elements of the fundamental representation of the Lie supergroup G are expressed in terms of functions on the product supermanifold G_0 x 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.
Cite
@article{arxiv.1201.4154,
title = {Invariant integration on orthosymplectic and unitary supergroups},
author = {Kevin Coulembier and Ruibin Zhang},
journal= {arXiv preprint arXiv:1201.4154},
year = {2015}
}