Arkiv för Matematik

A remark on local-global principles for conjugacy classes

Yuval Z. Flicker

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Abstract

A local-global principle is shown to hold for all conjugacy classes of any inner form of GL(n), SL(n), U(n), SU(n), and for all semisimple conjugacy classes in any inner form of Sp(n), over fields k with vcd(k)≤1. Over number fields such a principle is known to hold for any inner form of GL(n) and U(n), and for the split forms of Sp(n), O(n), as well as for SL(p) but not for SL(n), n non-prime. The principle holds for all conjugacy classes in any inner form of GL(n), but not even for semisimple conjugacy classes in Sp(n), over fields k with vcd(k)≤2. The principle for conjugacy classes is related to that for centralizers.

Article information

Source
Ark. Mat., Volume 40, Number 1 (2002), 47-53.

Dates
Received: 4 September 2000
Revised: 10 October 2000
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898752

Digital Object Identifier
doi:10.1007/BF02384501

Mathematical Reviews number (MathSciNet)
MR1948885

Zentralblatt MATH identifier
1075.14505

Rights
2002 © Institut Mittag-Leffler

Citation

Flicker, Yuval Z. A remark on local-global principles for conjugacy classes. Ark. Mat. 40 (2002), no. 1, 47--53. doi:10.1007/BF02384501. https://projecteuclid.org/euclid.afm/1485898752


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