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Parabolic Subgroup
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Summary
A
Parabolic Subgroup
is a type of
Subgroup of a semisimple algebraic group
that contains a
Borel Subgroup
, and it plays a crucial role in the
Structure theory of algebraic groups
. These subgroups are significant in
Representation Theory
and the
Study of flag varieties
, providing a bridge between
Algebraic Geometry
and
Group Theory
.
Concepts
Semisimple Algebraic Group
Borel Subgroup
Flag Variety
Representation Theory
Root System
Levi Decomposition
Algebraic Geometry
Lie Algebra
Bruhat Decomposition
Borel Subgroups
Reductive Group
Tits System
Relevant Degrees
Algebra 100%
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