Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-02-14
J.Math.Phys. 38 (1997) 5319-5349
Physics
High Energy Physics
High Energy Physics - Theory
56 pages, LaTeX, changes only in the writing of the title
Scientific paper
10.1063/1.531945
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.
Alfaro Jorge
Medina Ricardo
Urrutia Luis F.
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