Trigonometric solutions of triangle equations. Simple Lie superalgebras

Journal Article · Wed Jun 01 04:00:00 EDT 1988 · Theor. Math. Phys.; (United States)

OSTI ID:5960275

Bazhanov, V V; Shadrikov, A G

Trigonometric solutions of the graded triangle equation are constructed for the fundamental representations of all simple (nonexceptional) Lie superalgebras with nondegenerate metric. In Sec. 1, we introduce the concept of Z/sub 2/ graded spaces and give the basic definitions. In Sec. 2, we determine fundamental representations of the Lie superalgebras sl(m/vert bar/n) and osp(2r/vert bar/s) and give explicit realizations of the Coxeter automorphisms. In secs. 3 and 4, we give the trigonometric solutions of the graded triangle equation (quantum R matrices).

• Research Organization: Institute of High Energy Physics, Serpukhov (USSR)
• OSTI ID: 5960275
• Journal Information: Theor. Math. Phys.; (United States), Journal Name: Theor. Math. Phys.; (United States) Vol. 73:3; ISSN TMPHA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSICAL MECHANICS
COMMUTATORS
EQUATIONS
FIELD THEORIES
GRADED LIE GROUPS
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
METRICS
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
R MATRIX
SEMICLASSICAL APPROXIMATION
SYMMETRY GROUPS
TENSORS
UNITARITY
VECTORS