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Results tagged with rt.representation-theory
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user 54475
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
22
votes
1
answer
1k
views
Weyl group actions on 0-weight spaces
For a complex simple Lie group G with a maximal torus T, we can take a highest-weight representation V of G and look at the 0-weight space, i.e. the subspace of V of elements invariant under T. This s …
- 52.9k
8
votes
0
answers
568
views
Generators for invariant tensors of lie algebras
EDITED FOR (hopeful) CLARITY:
For a simple Lie algebra $\mathfrak{g}$ (over $\mathbb{C}$) and its adjoint group G, the $G$-invariant polynomials on $\mathfrak{g}$ are linear combinations of products …
- 301