Growth in Chevalley groups relatively to parabolic subgroups and some applications
Ilya D. Shkredov
Steklov Mathematical Institute, Moscow, Russia
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Abstract
Given a Chevalley group and a parabolic subgroup , we prove that for any set there is a certain growth of relatively to , namely, either or is much larger than . Also, we study a question about the intersection of with parabolic subgroups for large . We apply our method to obtain some results on a modular form of Zaremba’s conjecture from the theory of continued fractions, and make the first step towards Hensley's conjecture about some Cantor sets with Hausdorff dimension greater than .
Cite this article
Ilya D. Shkredov, Growth in Chevalley groups relatively to parabolic subgroups and some applications. Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 1945–1973
DOI 10.4171/RMI/1344