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Results tagged with rt.representation-theory
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user 39310
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
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Can $T$ act trivial in a repn of SL$_2(\mathbb{Z}_N)$?
I am confronted with the following problem:
If $\rho : \text{SL}_2(\mathbb{Z}) \to \text{GL}_{\mathbb{C}}(V)$ is a finite dimensional representation such that $\text{ker}(\rho)$ contains the principa …
- 334
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Can $T$ act trivial in a repn of SL$_2(\mathbb{Z}_N)$?
Let us assume $N = p^e$ for some prime $p$ (not necessarily odd). By this paper Lemma 3.1,
$$\overline{\langle \langle T^M \rangle \rangle} = \Gamma(M, \mathbf{Z_p}) = \{ \alpha = \begin{pmatrix} a …
- 334
2
votes
1
answer
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Modular Forms w.r.t. different representations linearly independent?
Let $V$ be a finite dimensional vector space over $\mathbb{C}$. Let $G = \text{SL}_2(\mathbb{Z})$, say, and $\rho : G \to \text{GL}_\mathbb{C}(V)$ a representation. Let us take a fixed basis $b_1, ... …
- 334