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Journal of Lie Theory 31 (2021), No. 1, 189--220
Copyright Heldermann Verlag 2021

Notes on Harish-Chandra Cells of (sp(2n, C), GL(n, C))-Modules

Leticia Barchini
Mathematics Department, Oklahoma State University, Stillwater, OK 74078, U.S.A.

We fix (G,K) = (Sp(2n, C), GL(n, C))). Cells of Harish-Chandra modules partition the set of irreducible Harish-Chandra 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 Harish-Chandra cells representations. The point of these notes is two-fold. We give closed formulae for the number of isomorphic cell representations. In Section 5 we give a parametrization of Harish-Chandra 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

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