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Why is $(\textrm{Ker } \beta)^0 = (\textrm{Ker } \alpha)^0$

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#algebraic-geometry #algebraic-groups #root-systems
242
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The root datum of a connected algebraic group, a few questions

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#lie-algebras #algebraic-groups #root-systems
479
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The Weyl group preserves inner product

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#lie-algebras #root-systems
553
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Why is the dual space of Cartan subalgebra an irreducible representation of Weyl group

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#representation-theory #lie-groups #lie-algebras #root-systems
1.8k
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Classifying all rank 2 and 3 root systems

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#abstract-algebra #representation-theory #lie-groups #lie-algebras #root-systems
1.7k
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How to find root subgroups

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#algebraic-groups #root-systems
524
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Same Dynkin diagrams $\Longrightarrow$ Isomorphic root systems.

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#lie-algebras #root-systems
454
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the orbit of a root under operations of irreducible crystallographic group?

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#abstract-algebra #group-theory #finite-groups #root-systems #coxeter-groups
2.8k
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Relation between root systems and representations of complex semisimple Lie algebras

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#representation-theory #lie-algebras #roots #root-systems
684
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Weyl group of a restricted root system

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#lie-algebras #root-systems
197
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What is the structure of the Coxeter groups of type $\text{D}_n$

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#group-theory #root-systems #coxeter-groups
672
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Dimension of the root spaces of a semisimple complex Lie algebra

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#lie-algebras #root-systems #semisimple-lie-algebras
936
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Why is a root system irreducible iff its Dynkin diagram is connected?

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#lie-algebras #root-systems
68
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Relationship between invariants of a simple algebraic group

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#abstract-algebra #group-theory #lie-algebras #algebraic-groups #root-systems
950
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Weyl group of orthogonal group

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#algebraic-groups #root-systems

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