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A two-sided cell in an affine Weyl group. II. (English) Zbl 0613.20026

The present paper is a continuation of the author’s former paper [(*) Part I, ibid. (to appear; Zbl 0598.20045)]. One of the main themes in (*) was to find a two-sided cell, written \(W_{(\nu)}\), of an affine Weyl group and to give an upper bound for the number of left cells in \(W_{(\nu)}\). In the present paper, we shall describe all left cells of \(W_ a\) in \(W_{(\nu)}\) and shall give the accurate number of left cells in \(W_{(\nu)}\).

MSC:

20G05 Representation theory for linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields
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