Twisted affine Lie superalgebras and integrability

Abstract

A twisted affine Lie superalgebra is either a twisted affine Lie algebra or of one of the types X = A ( 2 m − 1 , 2 n − 1 ) ( 2 ) ( m , n ≠ 0 , ( m , n ) ≠ ( 1 , 1 ) ), A ( 2 m , 2 n ) ( 4 ) , A ( 2 m , 2 n − 1 ) ( 2 ) or D ( m + 1 , n ) ( 2 ) ( m ≥ 0 , n > 0 ). It is known that irreducible integrable highest weight modules over a twisted affine Lie superalgebra of type X do not exist if m ≠ 0. In this paper, we show that nonzero level irreducible integrable finite weight modules over a twisted affine Lie superalgebra of type X do not exist if m ≠ 0.