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{wiki=Bruhat_decomposition}

For a connected reductive algebraic group, a <Borel subgroup> $B$, and a maximal torus $T\subseteq B$, the <Weyl group> $W=N_G(T)/T$ indexes the double cosets:
$$
G=\bigsqcup_{w\in W}B\dot wB.
$$

Bruhat decomposition of a reductive algebraic group

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 167 / 4 / iv / Solution

Bruhat decomposition of a reductive algebraic group

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Bruhat decomposition of a reductive algebraic group

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