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The relationship between the Weyl group and Isometries of a Maximal Flat

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#differential-geometry #lie-groups #weyl-group
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
223
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Weyl chambers associated to a root system

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#lie-algebras #root-systems #weyl-group
98
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Eigenvalues of elements of a Weyl group

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#eigenvalues-eigenvectors #roots #trace #reflection #weyl-group
59
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Identify some Coxeter group

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#matrices #group-theory #lie-algebras #semidirect-product #weyl-group
182
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Find a special element in weyl group

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#abstract-algebra #lie-algebras #symmetric-groups #weyl-group
524
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Automorphism in Weyl group of root system and its extension to Lie algebra

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#lie-algebras #root-systems #weyl-group
318
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Realizing automorphism in Weyl group as automorphism of Lie algebra

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#lie-algebras #root-systems #weyl-group
125
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Conjugating the longest element of a parabolic subgroup by longest element in larger parabolic?

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#abstract-algebra #finite-groups #reflection #coxeter-groups #weyl-group
1.4k
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What is the order of the Weyl group?

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#abstract-algebra #finite-groups #representation-theory #lie-algebras #weyl-group
360
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Schur-Weyl Duality (Example for k = 3)

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#representation-theory #tensor-products #tensor-decomposition #weyl-group
709
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Longest element of Weyl Group for $G_2$

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#group-theory #finite-groups #lie-algebras #weyl-group
546
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About parabolic subgroup of a Weyl group

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#abstract-algebra #group-theory #root-systems #coxeter-groups #weyl-group
682
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Which roots are fixed by simple reflections of the Weyl Group?

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#lie-algebras #root-systems #weyl-group #semisimple-lie-algebras
1.6k
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Irreducible Dual Representation

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#representation-theory #lie-algebras #weyl-group #semisimple-lie-algebras

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