9
votes
1answer
218 views

Representation varieties of 3-manifold groups in SL(n,C)

I am looking at the variety of representations of the fundamental group of a hyperbolic 3-manifold into $SL(n,C)$: $$Hom(\pi_1M, SL(n,{\mathbb C}))$$ It is known that volume and Chern-Simons ...
9
votes
4answers
402 views

When are those subgroups of $\mathrm{SL}(2, \mathbb{C})$ discrete?

Let $A = \pmatrix{1 & 0 \\ \alpha & 1} $ and $ B = \pmatrix{1 & 1 \\ 0 & 1}$, where $\alpha \in \mathbb{C}$ is a complex parameter. Now consider the family of representations ...
1
vote
0answers
125 views

How to pick out harmonics based on boundary conditions?

(..this is almost a continuation of my last question (which got closed!)...) Let me first rewrite one of the main results of this paper, http://calvino.polito.it/~camporesi/JMP94.pdf in a coordinate ...
2
votes
1answer
115 views

The measure on the harmonic spectrum from Selberg trace formula

One can see the following two equations, Theorem 6.1 (Selberg Trace formula) on page 26 of these notes. Equation 3.19 and 3.20 on page 11 of this paper. I vaguely feel that these two are the ...
0
votes
0answers
70 views

Existence of special pants decompositions for non-elementary representations into PSL(2,R)

A Theorem by Gallo, Goldman and Porter states the following: Let $S_g$ be a closed orientable surface of genus $g$ with fundamental group $\Gamma_g$, and fix a non-elementary representation ...
6
votes
1answer
339 views

Previous work on this generalization of continued fractions?

The 2x2 matrix representation of a continued fraction makes it clear that we're multiplying together a bunch of group elements. Inversion is essentially freely adjoining a generator to a Coxeter ...
5
votes
1answer
582 views

Finite dimensional spherical representation of $SO(n,1)(\mathbb{R})$

I'm looking for an explicit description of all the finite dimensional irreducible representation of the Lie group $SO(n,1)(\mathbb{R})$. Can you tell me, where I can find this description ? Thank you. ...
7
votes
2answers
442 views

Weil's theorem about maps from a discrete group to a Lie group.

Let K be a group (with discrete topology), G be a Lie group. Let $\operatorname{Hom}(K,G)$ be the space of all group homomorphisms from K to G. This is a closed subvariety of the space of all the maps ...