Journal of Lie Theory 24 (2014), No. 4, 1033--1046
Copyright Heldermann Verlag 2014
Radial Operators on Lie Supergroups and Characters of Representation
Alan Huckleberry
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum, Germany
and: School of Science and Engineering, Jacobs University, Campus Ring 1, 28759 Bremen, Germany
ahuck@cplx.rub.de
Matthias Kalus
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum, Germany
Matthias.Kalus@rub.de
Foundational material on radial operators on complex Lie supergroups is presented. In particular, a local version of Berezin's recursion formula for describing the radial parts of fundamental operators in general linear and ortho-symplectic cases is proved. Results which are suitable for applications for computing characters which are only defined on proper subdomains or covering spaces thereof are established.
Keywords: Complex Lie supergroups, radial operators, characters, Casimir operators.
MSC: 32C11, 81R05, 17B15
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