Representations of supergroups

Journal Article · Sat Aug 01 04:00:00 EDT 1981 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525127· OSTI ID:6248405

Balantekin, A B; Bars, I

An explicit construction of representations of supergroups is given in terms of direct products of covariant and contravariant fundamental representations. The rules of supersymmetrization are characterized by extended Young supertableaux. This constructive approach leads to explicit transformation properties of higher representations as well as to closed explicit formulas for characters from which other invariants such as dimensions and eigenvalues of all Casimir operators can be calculated. We have applied this approach so far to the supergroups SU(N/M), OSP(N/2M), P(N), for which we have obtained all the representations constructible as direct products of the fundamental (defining) representations. An argument is presented toward the irreducibility of all these representations.

• Research Organization: Wright Nuclear Structure Laboratory, Physics Department, Yale University, New Haven, Connecticut 06520
• DOE Contract Number: EY-76-C-02-3075
• OSTI ID: 6248405
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 22:8; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645301* -- High Energy Physics-- Particle Invariance Principles & Symmetries-- General-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CASIMIR OPERATORS
EIGENVALUES
GRADED LIE GROUPS
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL OPERATORS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS