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Parabolic subgroups of Vershik-Kerov's group
Author(s):
Waldemar
Holubowski
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2579-2582.
MSC (2000):
Primary 20H25, 20E15
Posted:
March 15, 2002
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Abstract:
In this note we show that all parabolic subgroups of Vershik-Kerov's group  (i.e. subgroups containing  --the group of infinite dimensional upper triangular matrices) are net subgroups for a wide class of semilocal rings  .
References:
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- 1.
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- 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.
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- 4.
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 ubowski, 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
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- 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
Email:
wholub@polsl.gliwice.pl
DOI:
10.1090/S0002-9939-02-06397-9
PII:
S 0002-9939(02)06397-9
Keywords:
Parabolic subgroup,
net subgroup
Received by editor(s):
March 22, 2001
Received by editor(s) in revised form:
May 10, 2001
Posted:
March 15, 2002
Dedicated:
Dedicated to Z. I. Borevich {(1922-1995)}
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2002,
American Mathematical Society
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