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A new characterization of the Bruhat decomposition

Published online by Cambridge University Press:  22 January 2016

Yoshifumi Kato
Yoshifumi Kato*
Affiliation:
Nagoya University
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By an algebraic homogeneous space, we mean the factor space X = G/P, where G is a simply-connected, complex, semi-simple Lie group and P is a parabolic subgroup of G. Many typical manifolds such as the projective spaces and the Grassmann varieties belong to this class of manifolds. For instance, the Grassmann variety G(k, n) can be expressed as SL(n + 1, C)/P, where P is a maximal parabolic subgroup of SL(n + 1, C) leaving a suitable k + 1 dimensional subspace invariant. In this paper, we devote ourselves to study the Bruhat decomposition of an algebraic homogeneous space X = G/P.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 86 , June 1982 , pp. 131 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

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