
Journal of Lie Theory 31 (2021), No. 1, 189220 Copyright Heldermann Verlag 2021 Notes on HarishChandra Cells of (sp(2n, C), GL(n, C))Modules Leticia Barchini Mathematics Department, Oklahoma State University, Stillwater, OK 74078, U.S.A. leticia@math.okstate.edu We fix (G,K) = (Sp(2n, C), GL(n, C))). Cells of HarishChandra modules partition the set of irreducible HarishChandra modules having the same infinitesimal character as the trivial representation. Irreducible modules in a cell form a basis of a representation of the complex Weyl group. These representations are the HarishChandra cells representations. The point of these notes is twofold. We give closed formulae for the number of isomorphic cell representations. In Section 5 we give a parametrization of HarishChandra cells. We use our results to compute the number of Unipotent representations attached to even nilpotent orbits. Keywords: Coherent continuation, Lusztig left cells. MSC: 22E47 [ Fulltextpdf (247 KB)] for subscribers only. 