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parabolic subgroup

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Definition

Given a linear algebraic group GG (i.e. an algebraic subgroup of GL(n,k)GL(n,k) where kk is a field), a subgroup PGP\subset G is said to be parabolic if it is closed in Zariski topology and the quotient variety G/PG/P is projective. A minimal (with respect to inclusion) parabolic subgroup of a linear algebraic group is called a Borel subgroup; in fact, given a Borel subgroup BB, any closed subgroup PBP\supset B is parabolic.

References

Revised on October 30, 2013 00:22:53 by Urs Schreiber (82.169.114.243)