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The orthogonality relations for the supergroup \(U(m | n)\). (English) Zbl 0873.22009

This paper is a continuation of another work by the same authors [J. Math. Phys. 36, 3085-3093 (1995; Zbl 0857.15016)], and the interested reader can have a look at the comment on this paper by T. Guhr [J. Math. Phys. 37, 3099 (1996)]and at the reply to that comment by the authors [J. Math. Phys. 37, 3100-3101 (1996)], in which they have extended the Itzykson-Zuber integral to the case of the unitary supergroup U(m{}n). The main observation is that in many cases the integration over the left- and right-invariant measure [dU] of the supermatrix elements will be automatically zero due to the presence of odd (Grassmannian) type variables. The authors have found the way to characterize those representations which produce non-zero values and they have determined the corresponding normalization coefficients.
Reviewer: I.Mladenov (Sofia)

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
81Q60 Supersymmetry and quantum mechanics
15B52 Random matrices (algebraic aspects)

Citations:

Zbl 0857.15016
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