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Highest weight of the $27$-dimensional representation of $E_6$

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#representation-theory #lie-groups
499
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Decomposition of universal enveloping algebra of the general linear Lie algebra

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#combinatorics #representation-theory #lie-groups #lie-algebras #homological-algebra
99
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Elements in $U(n)$

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#lie-groups #lie-algebras
1.3k
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Left-invariant vector fields versus right-invariant vector fields

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#lie-groups #lie-algebras #vector-fields
525
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Unipotent elements in a Lie group

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#lie-groups #lie-algebras #unipotent-matrices
2.9k
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Why $SO(3,\mathbb{R})$ is $3$-dimensional?

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#analysis #lie-groups
50
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Two questions on connected nilpotent Lie groups

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#lie-groups
1.5k
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Why is $\mathbb R$ \ ${0}$ open in R

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#manifolds #lie-groups
66
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What is the Lie group defined by 2 x 2 matricies?

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#lie-groups
229
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Proving the exponent of an element of a the Lie Algebra is an element of the Lie group.

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#differential-geometry #proof-verification #lie-groups #lie-algebras #matrix-exponential
212
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Finite-dimensional irreducible representation with non-vanishing zero weight space

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#abstract-algebra #representation-theory #lie-groups #lie-algebras #homological-algebra
408
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Universal enveloping algebra vs algebra of continuous functions

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#linear-algebra #lie-groups #hopf-algebras #quantum-groups
180
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Classify cohomogeneity one actions up to what?

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#differential-geometry #lie-groups #group-actions
1.8k
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Embedding of a subgroup into a group

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#group-theory #lie-groups #normal-subgroups
73
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The (orbifold) space of symmetric complex matrix 2

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#linear-algebra #group-theory #differential-geometry #manifolds #lie-groups

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