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Group‐Theoretical Approach to Extended Conformal Supersymmetry: Function Space Realizations and Invariant Differential Operators
Author(s) -
Dobrev V. K.,
Petkova V. B.
Publication year - 1987
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190350705
Subject(s) - indecomposable module , mathematics , invariant (physics) , pure mathematics , supergroup , differential operator , lie superalgebra , conformal map , superalgebra , conformal symmetry , lie group , lie algebra , conformal group , algebra over a field , mathematical physics , mathematical analysis , current algebra , affine lie algebra , geochemistry , geology
We give function space realizations of all representations of the conformal superalgebra su (2,2/ N ) and of the supergroup SU (2, 2 / N ) induced from irreducible finite‐dimensional Lorentz and SU ( N ) representations realized without spin and isospin indices. We use the lowest weight module structure of our su (2,2/ N ) representations to present a general procedure (adapted from the semisimple Lie algebra case) for the canonical construction of invariant differential operators closely related to the reducible (indecomposable) representations. All conformal supercovariant derivatives are obtained in this way. Examples of higher order invariant differential operators are given.