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On the left cells of Weyl groups. (Sur les cellules gauches des groupes de Weyl.) (French) Zbl 0615.20020
Let \(W\) be a Weyl group. In [Characters of reductive groups over a finite field (Ann. Math. Stud. 107, 1984; Zbl 0556.20033)], the author associated each left cell \(\Gamma\) of \(W\) with a \(\mathbb{C}[W]\)-module \([\Gamma]\) and then he proved that any constructible representation of \(W\) has the form \([\Gamma]\) for some left cell \(\Gamma\) of \(W\). In the present paper, the author proves the converse that the \(\mathbb{C}[W]\)-modules \([\Gamma]\) are constructible for all left cells \(\Gamma\) of \(W\). Since the structures of all constructible representations of \(W\) are known, the above result can be regarded as an explicit description of the \(\mathbb{C}[W]\)-modules \([\Gamma]\) with \(\Gamma\) the left cells of \(W\).
Reviewer: Shi Jianyi

20G05 Representation theory for linear algebraic groups