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At most two values for the length of the roots in an irreducible root system

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#representation-theory #lie-algebras #root-systems
122
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coefficients of the sum of roots corresponding to a parabolic subgroup

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#representation-theory #lie-groups #root-systems #homogeneous-spaces
486
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Why is a root system called a "root" system?

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#representation-theory #terminology #lie-algebras #root-systems #semisimple-lie-algebras
597
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The Weyl group of $\Phi$ permutes the set $\Phi$

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#lie-algebras #root-systems
164
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$sn: W\rightarrow \{1,-1\},sn(\sigma)=(-1)^{l(\sigma)}$ is a homomorphism

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#lie-algebras #root-systems #weyl-group
49
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Isomorphism question if base $\Delta$ for a root system is equal to the set of positive roots.

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#lie-algebras #root-systems
50
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Order of $z\in Z(W)\backslash \{\rm{id}\}$ for $W$ the Weyl group.

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#lie-algebras #root-systems
437
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Every maximal toral subalgebra is the centralizer of some $1$-dimensional subalgebra

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#lie-algebras #root-systems
713
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What is a Minimal Parabolic Subalgebra?

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#lie-groups #lie-algebras #root-systems
447
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Serre's theorem

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#lie-algebras #root-systems
102
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Does this root system come from a Lie group?

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#reference-request #lie-groups #lie-algebras #root-systems
284
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How does an automorphism of a semisimple Lie algebra induce an isomorphism of the root systems?

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#lie-algebras #root-systems
223
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Weyl chambers associated to a root system

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#lie-algebras #root-systems #weyl-group
67
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What does it mean to say that a semisimple Lie algebra is \textit{generated} by root spaces?

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#lie-algebras #root-systems
53
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Root systems and distinguished bases

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#lie-algebras #root-systems

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