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Standard set of Generators

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#lie-algebras #root-systems
392
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Why do Ad(K) orbits in the $-1$ eigenspace of a Cartan decomposition intersect the Weyl chamber once?

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#representation-theory #lie-groups #lie-algebras #ergodic-theory #root-systems
791
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Relation between simple roots and fundamental weights.

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#group-theory #lie-groups #lie-algebras #root-systems
2.3k
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Why are root spaces of root decomposition of semisimple Lie algebra 1 dimensional?

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#lie-groups #lie-algebras #root-systems
268
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Representing Petersen graph in root system $E_6$

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#graph-theory #algebraic-graph-theory #root-systems
710
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Given Cartan matrix, find root and Dynkin diagram

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#lie-groups #root-systems #dynkin-diagrams
175
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Is the sum of coroots the coroot of the sum?

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#representation-theory #lie-algebras #root-systems
49
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When is the group action transitive?

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#group-actions #reflection #root-systems #coxeter-groups
266
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Unique maximal short root

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#root-systems
147
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Show that every dominant fundamental weight is decomposed as a positive rational sum of roots.

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#representation-theory #lie-algebras #root-systems
86
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What is the basis of the root space $\mathfrak g_\theta$, where $\theta = \alpha_1+\cdots+\alpha_n$?

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#lie-algebras #root-systems
149
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How can we explain this symmetry in counting the number of positive roots?

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#representation-theory #lie-algebras #root-systems #dynkin-diagrams
394
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Exercise on root system of type $A_n$

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#lie-algebras #root-systems #weyl-group #dynkin-diagrams
200
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Extending base vector field via tensorproduct from $\mathbb{Q}$ to $\mathbb{R}$

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#linear-algebra #vector-spaces #field-theory #root-systems
35
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Reference for application of the theory of weights and weight-spaces to $\mathfrak{su}(2)$ and $\mathfrak{su}(3)$

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#reference-request #lie-algebras #root-systems

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