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1999 On special pieces in the unipotent variety
Meinolf Geck, Gunter Malle
Experiment. Math. 8(3): 281-290 (1999).


This article is the result of experiments performed using computer programs written in the GAP language. We describe an algorithm which computes a set of rational functions attached to a finite Coxeter group W. Conjecturally, these rational functions should be polynomials, and in the case where W is the Weyl group of a Chevalley group G defined over $\mathbb F_q$, the values of our polynomials at q should give the number of $\mathbb F_q$-rational points of Lusztig's special pieces in the unipotent variety of G. The algorithm even works for complex reflection groups. We give a number of examples which show, in particular, that our conjecture is true for all types except possibly $B_n$ and $D_n$.


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Meinolf Geck. Gunter Malle. "On special pieces in the unipotent variety." Experiment. Math. 8 (3) 281 - 290, 1999.


Published: 1999
First available in Project Euclid: 9 March 2003

zbMATH: 0962.20033
MathSciNet: MR1724160

Primary: 20G15
Secondary: 20G05

Rights: Copyright © 1999 A K Peters, Ltd.


Vol.8 • No. 3 • 1999
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