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Fock representations of the Lie superalgebra q(n + 1)

By T Palev and J Van Der Jeugt

Abstract

For the Lie superalgebra q(n + 1) a description is given in terms of creation and annihilation operators, in such a way that the defining relations of q(n + 1) are determined by quadratic and triple supercommutation relations of these operators. Fock space representations Vp of q(n + 1) are defined by means of these creation and annihilation operators. These new representations are introduced as quotient modules of some induced module of q(n+1). The representations Vp are not graded, but they possess a number of properties that are of importance for physical applications. For p a positive integer, these representations Vp are finite-dimensional, with a unique highest weight (of multiplicity 1). The Hermitian form that is consistent with the natural adjoint operation on q(n + 1) is shown to be positive definite on Vp. For q(2) these representations are “dispin”. For the general case of q(n + 1), many structural properties of Vp are derived

Topics: Short title, The Lie superalgebra q(n + 1
Year: 1999
OAI identifier: oai:CiteSeerX.psu:10.1.1.236.8160
Provided by: CiteSeerX
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