15 May 2021 Kakutani equivalence of unipotent flows
Adam Kanigowski, Kurt Vinhage, Daren Wei
Author Affiliations +
Duke Math. J. 170(7): 1517-1583 (15 May 2021). DOI: 10.1215/00127094-2020-0074


We study Kakutani equivalence in the class of unipotent flows acting on finite-volume quotients of semisimple Lie groups. For every such flow, we compute the Kakutani invariant of M. Ratner, the value being explicitly given by the Jordan block structure of the unipotent element generating the flow. This, in particular, answers a question of M. Ratner. Moreover, it follows that the only loosely Kronecker unipotent flows are given by (1t01)×id acting on (SL(2,R)×G)Γ, where Γ is an irreducible lattice in SL(2,R)×G (with the possibility that G={e}).


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Adam Kanigowski. Kurt Vinhage. Daren Wei. "Kakutani equivalence of unipotent flows." Duke Math. J. 170 (7) 1517 - 1583, 15 May 2021. https://doi.org/10.1215/00127094-2020-0074


Received: 19 September 2018; Revised: 30 May 2020; Published: 15 May 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.1215/00127094-2020-0074

Primary: 37A35
Secondary: 37A20

Keywords: homogeneous dynamics , Kakutani equivalence , loosely Kronecker , unipotent flows

Rights: Copyright © 2021 Duke University Press

Vol.170 • No. 7 • 15 May 2021
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