Big elements in irreducible linear groups

Gordeev N, Rehmann U (2014)
Archiv der Mathematik 103(3): 201-210.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Gordeev, Nikolai; Rehmann, UlfUniBi
Abstract / Bemerkung
Let V be a linear space over a field K of dimension n > 1, and let be an irreducible linear group. In this paper we prove that the group G contains an element g such that rank for every , where E (n) is the identity operator on V. This estimate is sharp for any . The existence of such an element implies that the conjugacy class of G in GL(V) intersects the big Bruhat cell of GL(V) non-trivially (here B is a fixed Borel subgroup of G). The latter fact is equivalent to the existence of a complete flag such that the flags are in general position for some g a G.
Stichworte
Linear groups; Conjugacy classes; Complete flags; Bruhat cells
Erscheinungsjahr
2014
Zeitschriftentitel
Archiv der Mathematik
Band
103
Ausgabe
3
Seite(n)
201-210
ISSN
0003-889X
Page URI
https://pub.uni-bielefeld.de/record/2705630

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Gordeev N, Rehmann U. Big elements in irreducible linear groups. Archiv der Mathematik. 2014;103(3):201-210.
Gordeev, N., & Rehmann, U. (2014). Big elements in irreducible linear groups. Archiv der Mathematik, 103(3), 201-210. doi:10.1007/s00013-014-0679-4
Gordeev, N., and Rehmann, U. (2014). Big elements in irreducible linear groups. Archiv der Mathematik 103, 201-210.
Gordeev, N., & Rehmann, U., 2014. Big elements in irreducible linear groups. Archiv der Mathematik, 103(3), p 201-210.
N. Gordeev and U. Rehmann, “Big elements in irreducible linear groups”, Archiv der Mathematik, vol. 103, 2014, pp. 201-210.
Gordeev, N., Rehmann, U.: Big elements in irreducible linear groups. Archiv der Mathematik. 103, 201-210 (2014).
Gordeev, Nikolai, and Rehmann, Ulf. “Big elements in irreducible linear groups”. Archiv der Mathematik 103.3 (2014): 201-210.

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