RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Full text: PDF file (280 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
UDC: 512.817+515.178.7
Received: 18.05.2016

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
\Bibitem{VinSch17}
\by \`E.~B.~Vinberg, O.~V.~Schwarzman
\paper A Criterion of Smoothness at Infinity for an Arithmetic Quotient of the Future Tube
\jour Funktsional. Anal. i Prilozhen.
\yr 2017
\vol 51
\issue 1
\pages 40--59
\mathnet{http://mi.mathnet.ru/faa3263}
\crossref{https://doi.org/10.4213/faa3263}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3647781}
\elib{http://elibrary.ru/item.asp?id=28169174}
\transl
\jour Funct. Anal. Appl.
\yr 2017
\vol 51
\issue 1
\pages 32--47
\crossref{https://doi.org/10.1007/s10688-017-0166-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000396373700003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85015448163}


Linking options:
  • http://mi.mathnet.ru/eng/faa3263
  • https://doi.org/10.4213/faa3263
  • http://mi.mathnet.ru/eng/faa/v51/i1/p40

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:172
    References:14
    First page:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018