摘要
Let (G,G ′ ) be a reductive dual pair of a symplectic group and an orthogonal group defined over a finite field of odd characteristic with corresponding Frobenius maps F. The Howe correspondence establishes a correspondence between a subset of irreducible characters of G F and a subset of irreducible characters of G ′F . The Lusztig correspondence is a bijection between the Lusztig series indexed by the conjugacy class of a rational semisimple element s in the connected component (G∗) 0 of the dual group G ∗ of G and the set of unipotent characters of the centralizer CG ∗ (s) F . In this paper, we prove the commutativity (up to a twist of the sign character) between these two correspondences. As a consequence, the Howe correspondence can be explicitly described in terms of Lusztig’s parametrizations for classical groups.