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Results tagged with rt.representation-theory
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user 5952
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
3
votes
0
answers
316
views
When does Ext^2 vanish in a category of group representations.
Let $G$ be a linear algebraic group over field $k$ of characteristic zero. It is well known that the category of finite dimensional $k$--linear representations of $G$ is abelian, and that it is semisi …
- 4,015
9
votes
2
answers
512
views
Are algebraic groups defined by their invariants in tensor spaces?
Let $K$ be a field of characteristic zero, and let $G \subseteq \mathrm{GL}_V$ be an algebraic group over $K$, acting faithfully on a finite dimensional vector space $V$. Let $H \subseteq \mathrm{GL}_ …
- 4,015
3
votes
How ugly is the isomorphism R[GxH] = R[G] (X) R[H] for groups G, H?
As a partial answer to (2): If $k$ is algebraically closed (any characteristic) and $G$ and $H$ finite, then the tensor product of any irreducible $k$--representation $V$ of $G$ with any irreducible $ …
- 4,015
1
vote
Accepted
Points of reductive groups
A bit of Tannakian formalism clarifies the situation. Recall that for every abstract group $\Gamma$ there is a notion of "algebraic hull" $\Gamma^{alg}$ constructed as follows: Consider pairs $(\varph …
- 4,015
6
votes
Do representations of finite groups of Lie type preserve diagonalizable elements?
I think the answer is yes if and only if $k$ contains all $(q-1)$-st roots of unity, for the following reason:
If $D$ is a diagonal matrix in $SL_r(\mathbb F_q)$, then its order divides $q-1$ because …
- 4,015
18
votes
Tannaka formalism and the étale fundamental group
Besides that the theories (étale fundamental group and Tannakian formalism) just formally look alike, there exist actual comparison results between certain étale and Tannakian fundamental groups.
Nam …
- 4,015