Dimension and character formulas for Lie supergroups

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

DOI:https://doi.org/10.1063/1.525038· OSTI ID:6422615

Balantekin, A B; Bars, I

A character formula is derived for Lie supergroups. The basic technique is that of symmetrization and antisymmetrization associated with Young tableaux generalized to supergroups. We rewrite the characters of the ordinary Lie groups U(N), O(N), and Sp(2N) in terms of traces in the fundamental representation. It is then shown that by simply replacing traces with supertraces the characters of certain representations for U(N/M) and OSP(N/2M) are obtained. Dimension formulas are derived by calculating the characters of a special diagonal supergroup element with (+1) and (-1) eigenvalues. Formulas for the eigenvalues of the quadratic Casimir operators are given. As applications, the decomposition of a representation into representations of subgroups is discussed. Examples are given for the Lie supergroup SU(6/4) which has physical applications as a dynamical supersymmetry in nuclei.

• Research Organization: Physics Department, Yale University, New Haven, Connecticut 06511
• OSTI ID: 6422615
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 22:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
BOSONS
CASIMIR OPERATORS
EIGENVALUES
FERMIONS
GRADED LIE GROUPS
LIE GROUPS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL OPERATORS
SU GROUPS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
U GROUPS