Bruhat decomposition

Bruhat decomposition is the name for the fact that B\G/B=W, where G is a reductive group, B a Borel subgroup, and W the Weyl group. Less canonically, one can write G=BWB.

In the case of the general linear groupMathworldPlanetmath G=GLn, B is the group of nonsingular upper triangular matricesMathworldPlanetmath, and W is the collection of permutation matricesMathworldPlanetmath (and is isomorphicPlanetmathPlanetmathPlanetmath to Sn). Any nonsingular matrix can thus be written uniquely as a product of an upper triangular matrix, a permutation matrix, and another upper triangular matrix.

Title Bruhat decomposition
Canonical name BruhatDecomposition
Date of creation 2013-03-22 15:43:15
Last modified on 2013-03-22 15:43:15
Owner nerdy2 (62)
Last modified by nerdy2 (62)
Numerical id 9
Author nerdy2 (62)
Entry type Theorem
Classification msc 20-00