Canonical realizations of Lie superalgebras: Ladder representations of the Lie superalgebra A(m,n)
- 1 October 1981
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (10) , 2127-2131
- https://doi.org/10.1063/1.524781
Abstract
A simple formula for realizations of Lie superalgebras in terms of Bose and Fermi creation and annihilation operators is given. The essential new feature is that Bose and Fermi operators mutually anticommute. The Fock representation of these operators is used in order to construct a class of irreducible finite‐dimensional representations of the simple Lie superalgebra A(m,n). The matrix elements of the generators are written down. For m≳0 all representations turn out to be nontypical.Keywords
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