Basic representation of the affine superalgebra \(A^{(2)}(0,1)\)
In [\textit{G. Golitzin}, J. Algebra 117, No. 1, 198-226 (1988; Zbl 0652.17013)] the author constructed some irreducible highest weight representations of the affine superalgebras \(A^{(4)}(0,2l)\) and \(A^{(2)}(0,2l-1)\). Since his considerations degenerate for \(A^{(2)}(0,1)\), the purpose of the paper under review is to cover also this simplest case. The algebra \(\widetilde{\mathfrak g}(\nu)=A^{(2)}(0,1)\) is the extended twisted loop algebra associated with the finite dimensional simple superalgebra \({\mathfrak g}=A(0,1)=sl(1,2)\) and its Cartan automorphism \(\nu\). The irreducible modules given in the paper are those of fundamental highest weight. They are realized as the tensor product of symmetric and exterior algebras on which \(A^{(2)}(0,1)\) acts by products of vertex operators and operators of Clifford type.
scientific article; zbMATH DE number 1271651