Timeline for Linear irreducible representations of residually finite groups
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2011 at 7:31 | comment | added | Benjamin Hayes | I believe the standard definition is no closed $G$-invariant subspaces. | |
| May 21, 2011 at 16:26 | answer | added | Andreas Thom | timeline score: 2 | |
| May 15, 2011 at 3:57 | comment | added | Yemon Choi | To clarify: when you talk about an irreducible representation $\pi:G \to {\rm End}(V)$, do you mean that there is no proper $G$-invariant subspace other than zero, or do you mean that there is no proper, closed $G$-invariant subspace other than zero | |
| May 14, 2011 at 13:24 | comment | added | Alain Valette | Mark is right. Here is for example a nice result by Michael Cowling and Tim Steger: Let $G$ be a non-compact simple Lie group, and let $\pi$ be a unitary irreducible representation of $G$; assume that $\pi$ is not in the discrete series of $G$ (you exclude countably many rep's in a continuum). Then the restriction of $\pi$ to any lattice $\Gamma$ in $G$, is an irreducible representation of $\Gamma$. | |
| May 14, 2011 at 12:02 | comment | added | user6976 | How about the free group with two generators? Every representation of every 2-generated group is a representation of $F_2$. | |
| May 14, 2011 at 11:39 | history | asked | Sarah Wolfe | CC BY-SA 3.0 |