In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic groups G into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases. It is related to the Schubert cell decomposition of flag varieties: see Weyl group for this.
More generally, any group with a (B, N) pair has a Bruhat decomposition.
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In mathematics, the Bruhatdecomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic...
decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition)...
be considered as a special case of the Bruhatdecomposition. The Birkhoff decomposition, a special case of the Bruhatdecomposition for affine groups....
then we obtain the Bruhatdecomposition G = ⋃ w ∈ W B w B {\displaystyle G=\bigcup _{w\in W}BwB} which gives rise to the decomposition of the flag variety...
study of the Bruhat order on the Weyl group, and introduced the name "Bruhat order" because of the relation to the Bruhatdecomposition introduced by...
linear group that acts on it, similar questions are involved in the Bruhatdecomposition and classification of parabolic subgroups (as block triangular matrices)...
this is Bruhatdecomposition. Berenstein, Arkady; Fomin, Sergey; Zelevinsky, Andrei (2005), "Cluster algebras. III. Upper bounds and double Bruhat cells"...
Dmitri; Roetteler, Martin (2018). "Shorter stabilizer circuits via Bruhatdecomposition and quantum circuit transformations". IEEE Transactions on Information...
Birkhoff factorization together with the Bruhatdecomposition for the ordinary general linear group. Birkhoff decomposition (disambiguation) Riemann–Hilbert problem...
infinity. This argument gives one of the simplest examples of the Bruhatdecomposition: S L ( 2 , k ) = B ∪ B ⋅ J ⋅ B , {\displaystyle \displaystyle {\mathbf...
{\displaystyle \partial M=A\cup B} . See also Twisted Poincaré duality In the Bruhatdecomposition of the flag variety of a Lie group, the fundamental class corresponds...
upper triangular matrices. The double coset space B \ G / B is the Bruhatdecomposition of G. The double cosets are exactly BwB, where w ranges over all...
Compact group Cartan subgroup Cartan subalgebra Toral Lie algebra Bruhatdecomposition Weyl character formula Representation theory of a connected compact...
the double coset BsB is dense in G; this is a special case of the Bruhatdecomposition. Since ξ is fixed by B, the matrix coefficient ψ(g) is constant on...
w0 is the number of the positive roots. The open cell Bw0B in the Bruhatdecomposition of a semisimple algebraic group G is dense in Zariski topology; topologically...
groups over finite fields. Lang's theorem Generalized flag variety, Bruhatdecomposition, BN pair, Weyl group, Cartan subgroup, group of adjoint type, parabolic...
G the group of conformal transformations). Parabolic Lie algebra Bruhatdecomposition Robert J. Baston and Michael G. Eastwood, The Penrose Transform:...
24033/bsmf.2006, MR 0788969 Iwahori, N.; Matsumoto, H. (1965), "On some Bruhatdecomposition and the structure of the Hecke rings of p-adic Chevalley groups"...
Coxeter group, called the Weyl group of G. Then the group G has a Bruhatdecomposition G = ⨆ w ∈ W B w B {\displaystyle G=\bigsqcup _{w\in W}BwB} into double...
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