, Volume 52, Issue 3, pp 3178-3185

Bruhat decomposition decomposition of root semisimple subgroups in the special linear group

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Abstract

It is proved that the root semisimple subgroups in the special linear group over a field intersects at most four cosets in the Bruhat decomposition and, moreover, most elements of the given subgroup lie in the same coset, with the remaining elements lying in distinct cosets.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 239–246, 1987.