Finite-dimensional half-integer weight modules over queer Lie superalgebras

الأصل · EN

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra q(n). It is given in terms of Brundan's work of finite-dimensional integer weight q(n)-modules by means of Lusztig's canonical basis. Using this viewpoint we compute the characters of the finite-dimensional half-integer weight irreducible modules. For a large class of irreducible modules whose highest weights are of special types (i.e., totally connected or totally disconnected) we derive closed-form character formulas that are reminiscent of Kac-Wakimoto character formula for classical Lie superalgebras.