higher geometry / derived geometry
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Given a sequence of inclusions
where
$G$ is a connected complex reductive algebraic group
$B$ is a Borel subgroup
$T$ is a maximal torus;
this induces
the Weyl group $W_0 = N(T)/T$;
the character lattice $\mathfrak{h}_{\mathbb{Z}}^\ast = Hom(T, \mathbb{C}^\times)$;
the cocharacter lattice $\mathfrak{h}_{\mathbb{C}} = Hom(\mathbb{C}^\times, T)$.
a standard parabolic subgroup of $G$ is a subgroup $P_J$ including $B$ such that $G/P$ is a projective variety;
parabolic subgroup is one conjugate to the standard parabolic subgroup.
the flag variety $G/B$;
the partial flag varieties $G/P_J$
A Bruhat decomposition is, if it exists, a coproduct decomposition into a disjoint union of double cosets
with
$W_J \coloneqq \{v \in W_0 | v T \subset P_J\}$
$W^J \coloneqq \{coset\; representatives\; u \; of \; cosets \; in W_0/W_J\}$
into Schubert varieties
Last revised on August 2, 2017 at 12:40:28. See the history of this page for a list of all contributions to it.