Abstract
The Gelfand-Tzetlin method provides explicit coordinates on the parameter space of the unitary groupU(k) which make direct evaluations of group integrals possible. It is closely related to the Gelfand construction of finite-dimensional irreducible representations. We generalize the Gelfand-Tzetlin method to the unitary supergroupU(k 1/k2). The coordinates on the parameter space for supergroup integrals and the invariant Haar measure are evaluated. As an example, the supersymmetric Harish-Chandra-Itzykson-Zuber integral is calculated. A generalized Gelfand pattern containing anticommuting variables is introduced which determines the representation.
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Communicated by M. Jimbo
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Guhr, T. Gelfand-Tzetlin coordinates for the unitary supergroup. Commun.Math. Phys. 176, 555–576 (1996). https://doi.org/10.1007/BF02099250
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DOI: https://doi.org/10.1007/BF02099250