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Jan
30
revised $2$-cohomology group of semi-direct products
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Jan
30
revised $2$-cohomology group of semi-direct products
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Jan
30
answered $2$-cohomology group of semi-direct products
Jan
30
comment Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
@JimHumphreys: Corrected!
Jan
30
revised Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
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Jan
10
revised Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
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Jan
10
revised Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
Reference to Bourbaki corrected
Jan
10
revised Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
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Jan
9
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Jan
9
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Jan
9
comment Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
Idea of proof: One constructs a Lie subalgebra $\mathfrak{g}_1\subset \mathrm{Lie}\,G$ isomorphic to $\mathfrak{sl}_2$ and a $\mathfrak{g}_1$-invariant irreducible subspace $V_1\subset V$ with highest weight $\sigma(\lambda)$. The restriction of the bilinear form to $V_1$ is non-degenerate. .A $\mathfrak{g}_1$--invariant bilinear form on $V_1$ is symmetric if and only if $\sigma(\lambda)$ is even.
Jan
8
revised Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
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Jan
7
revised Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
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Jan
7
answered Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?
Dec
29
comment How to “lift” a transitive group action on a manifold?
Welcome to Math Overflow, @Dmitri Alekseevsky!
Dec
16
revised Reflex fields of Shimura varieties
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16
revised Reflex fields of Shimura varieties
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Dec
16
answered Reflex fields of Shimura varieties
Dec
7
comment Hua Luogeng's definition of automorphism group for Hermitian symmetric space
This formula is also given in Helgason's book "Differential Geometry, Lie Groups and Symmetric Spaces", AMS 2001, Exercise D.1 on page 526.
Dec
5
comment Counterexample request: Adjoint bundle has regular section, no Cartan reduction
If you really want to get an answer to your question, maybe you would like to edit your question and add details: what is $X$ (a scheme? a variety? over what field?), a principal bundle over what space and under what kind of group, what is the adjoint bundle, and what do you mean by a Cartan....