Orthogonality relations and supercharacter formulas of U(m{vert_bar}n) representations

Journal Article · Wed Oct 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531945· OSTI ID:587138

Alfaro, J ^[1]; Medina, R ^[2]; Urrutia, L F ^[3]

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1. Facultad de Fisica, Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)
2. Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 Sao Paulo, (Brazil)
3. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Circuito Exterior, C.U., Apartado Postal 70-543, 04510 (Mexico)

In this paper we obtain the orthogonality relations for the supergroup U(m{vert_bar}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{endash}Chandra{endash}Itzykson{endash}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{vert_bar}n) representations. A new way of labeling the U(m{vert_bar}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. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 587138
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
GROUP THEORY
IRREDUCIBLE REPRESENTATIONS
QUANTUM CHROMODYNAMICS
SUPERSYMMETRY
U GROUPS
UNITARY SYMMETRY