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intuition behind basis of a root system

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#lie-algebras #root-systems
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Which is the Weyl group of $U(n)$

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#lie-groups #lie-algebras #permutations #root-systems
302
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Weyl group and weight lattice chambers.

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#lie-algebras #integer-lattices #root-systems #coxeter-groups #lattices-in-lie-groups
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Under Langlands duality, which semisimple Lie groups are self-dual?

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#lie-groups #lie-algebras #duality-theorems #root-systems
108
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the real roots of a connected tame quiver

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#root-systems #quiver
187
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Any explicit pictures of root datum

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#lie-groups #root-systems
706
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Recover Lie algebra bracket from the root system

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#representation-theory #lie-algebras #root-systems #dynkin-diagrams
100
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Restrictions of representations of compact connected semisimple Lie groups to $SU(2)$ subgroups

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#lie-groups #root-systems #branching-rules
151
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Why are roots in representation theory called roots?

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#representation-theory #terminology #root-systems
256
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If $G$ is an algebraic group of adjoint type, is $\alpha_s^\vee(-1)=1$?

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#group-theory #representation-theory #algebraic-groups #root-systems #coxeter-groups
238
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If $\alpha,\beta$ are orthogonal simple roots, do the coroots $\alpha^\vee$ and $\beta^\vee$ commute?

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#representation-theory #root-systems #coxeter-groups
502
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Why is a Fundamental Dominant Weight a Weight?

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#root-systems
1.1k
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Why does the Killing form act on the Cartan subalgebra as $\kappa(h,k)=\sum_\alpha \alpha(h)\alpha(k)$?

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#lie-algebras #root-systems
149
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Reduced decomposition of an element in the Weyl group smaller length than it should have

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#lie-algebras #algebraic-groups #root-systems #reductive-groups #weyl-group
266
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direct sum and root system of a Lie algebra

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#lie-algebras #root-systems

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