A linear algebra description of Kc Gc/Bc for classical groups

摘要

For a symmetric subgroup Kc of a complex reductive group Gc, with Borel subgroup BC, the (finite) double coset space Kc Gc/Bc has been important in classifying the admissible representations of the real form of Gc associated to the pair (Gc, Kc). For classical groups Gc, we give a description of Kc Gc/Bc using standard tools of linear algebra. The description reveals a natural heierarchy of complexity among 7 of the 10 broad classes of classical symmetric pairs.