Alfaro, Jorge; Medina, Ricardo; Urrutia, Luis F. The orthogonality relations for the supergroup \(U(m | n)\). (English) Zbl 0873.22009 J. Phys. A, Math. Gen. 28, No. 16, 4581-4588 (1995). 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) Cited in 1 Document MSC: 22E70 Applications of Lie groups to the sciences; explicit representations 81Q60 Supersymmetry and quantum mechanics 15B52 Random matrices (algebraic aspects) Keywords:Quantum chromodynamics; unitary supergroup; supermatrix; Itzykson-Zuber integral Citations:Zbl 0857.15016 PDFBibTeX XMLCite \textit{J. Alfaro} et al., J. Phys. A, Math. Gen. 28, No. 16, 4581--4588 (1995; Zbl 0873.22009) Full Text: DOI arXiv