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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 1, Pages 40–59 (Mi faa3263)

A Criterion of Smoothness at Infinity for an Arithmetic Quotient of the Future Tube

È. B. Vinberga, O. V. Schwarzmanbc

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b National Research University "Higher School of Economics" (HSE), Moscow
c Independent University of Moscow

Abstract: Let $\Gamma$ be an arithmetic group of affine automorphisms of the $n$-dimensional future tube $\mathcal{T}$. It is proved that the quotient space $\mathcal{T}/\Gamma$ is smooth at infinity if and only if the group $\Gamma$ is generated by reflections and the fundamental polyhedral cone (“Weyl chamber”) of the group $d\Gamma$ in the future cone is a simplicial cone (which is possible only for $n\le 10$). As a consequence of this result, a smoothness criterion for the Satake–Baily–Borel compactification of an arithmetic quotient of a symmetric domain of type IV is obtained.

Keywords: symmetric domain, future tube, boundary component, arithmetic quotient, reflection group, automorphic form

DOI: https://doi.org/10.4213/faa3263

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English version:
Functional Analysis and Its Applications, 2017, 51:1, 32–47

Bibliographic databases:

Document Type: Article
UDC: 512.817+515.178.7

Citation: È. B. Vinberg, O. V. Schwarzman, “A Criterion of Smoothness at Infinity for an Arithmetic Quotient of the Future Tube”, Funktsional. Anal. i Prilozhen., 51:1 (2017), 40–59; Funct. Anal. Appl., 51:1 (2017), 32–47

Citation in format AMSBIB
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