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Results tagged with rt.representation-theory
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user 16143
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
7
votes
2
answers
418
views
Separating subspaces in an irreducible representation
Suppose $G$ is a semisimple $\mathbb{R}$-algebraic group with finite center, and suppose $G$ acts irreducibly on a vector space $V$. Suppose $U \subset V$ and $W \subset V$ are subspaces.
$\mathbf{Q …
- 3,201
23
votes
What invariants of a matrix or representation can be used to find its GL(n,Z)-conjugacy class?
In each conjugacy class you can always find a representative which is block upper triangular, and the diagonal blocks have irreducible characteristic polynomials. This gives a partial reduction to the …
- 3,201
9
votes
Are there some nontrivial group homomorphisms from $SL_n(\mathbb{Z})$ to $GL_{n-1}(\mathbb{Z...
By the Margulis superrigidity theorem, any homomorphism from $SL(n,\mathbb{Z})$ to $SL(n-1,\mathbb{R})$ with infinite image has to extend to a homomorphism from $SL(n,\mathbb{R})$ to $SL(n-1,\mathbb{R …
- 3,201
13
votes
Accepted
Lattices in $SL(n,\mathbb R)$
The answer is yes. It is theorem [2.13] of the following paper of Prasad and Raghunathan:
Prasad, Gopal; Raghunathan, M. S. Cartan subgroups and lattices in semi-simple groups. Ann. of Math. (2) 96 ( …
- 3,201