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Parabolic subgroups of Vershik-Kerov's group

Author: Waldemar Holubowski
Journal: Proc. Amer. Math. Soc. 130 (2002), 2579-2582
MSC (2000): Primary 20H25, 20E15
Published electronically: March 15, 2002
MathSciNet review: 1900864
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Abstract: In this note we show that all parabolic subgroups of Vershik-Kerov's group $GLB(R)$ (i.e. subgroups containing $T(\infty,R)$--the group of infinite dimensional upper triangular matrices) are net subgroups for a wide class of semilocal rings $R$.

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  • 1. J. L. Alperin, R. B. Bell, Groups and representations, Springer-Verlag New York Berlin Heidelberg, 1995. MR 96m:20001
  • 2. Z.I.Borevich, On parabolic subgroups in linear groups over a semilocal ring, (Russian) Vestnik Leningr. Univ., Mat. Meh. Astr. 13 (1976) 16-24 (English translation: Vestn. Leningr. Univ., Math. 9 (1981) 187-196). MR 57:6217
  • 3. N. Bourbaki, Groupes et algebres de Lie, Chap.IV Groupes de Coxeter and systemes de Tits, Hermann Paris, 1968. MR 39:1590
  • 4. W.Ho\lubowski, Subgroups of infinite triangular matrices containing diagonal matrices, to appear in Publ. Math. Debrecen. 59 (2001). CMP 2002:01
  • 5. N.A.Vavilov, Bruhat decomposition for subgroups containing the group of diagonal matrices. (Russian) Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklova 114 (1982) 50-61 (English translation: J. Sov. Math. 27 (1984) 2865-2874). MR 84e:20050
  • 6. A. M. Vershik, S. V. Kerov, On an infinite-dimensional group over a finite field.(Russian) Funktsional. Anal. i Prilozhen. 32 (1998), no. 3, 3-10, 95 (English translation: Funct. Anal. Appl. 32 (1998), no. 3, 147-152 (1999)). MR 2000b:22006

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Additional Information

Waldemar Holubowski
Affiliation: Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Keywords: Parabolic subgroup, net subgroup
Received by editor(s): March 22, 2001
Received by editor(s) in revised form: May 10, 2001
Published electronically: March 15, 2002
Dedicated: Dedicated to Z. I. Borevich (1922-1995)
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society

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