an:03995965
Zbl 0615.20020
Lusztig, George
On the left cells of Weyl groups
FR
C. R. Acad. Sci., Paris, S??r. I 302, 5-8 (1986).
00151360
1986
j
20G05
Weyl groups; constructible representations; left cells
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 \(W\).
Shi Jianyi
Zbl 0556.20033