All Questions
Tagged with automorphic-forms lie-groups
7 questions with no upvoted or accepted answers
11
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Why are there so few irreducible admissible representations of $\text{GL}(n,\mathbb{R})$ (up to infinitesimal equivalence)?
Studying Langlands's classification of irreducible admissible representations, I have been rather stunned by the following:
Theorem
Up to infinitesimal equivalence, all irreducible admissible ...
- 511
6
votes
0
answers
1k
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Definition of Admissible Representation
Let $G$ be a connected, reductive group over a number field $k$. Let $v$ be a place of $k$.
If $v$ is finite, an admissible representation of $G(k_v)$ is defined to be an abstract representation of $...
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3
votes
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188
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Non-vanishing of left- vs. right-averages over lattices in $SL(2,\mathbb{R})$
I asked the same question on MSE one week ago, but it has not received any answers.
Background. Let $G=SL(2,\mathbb{R})$, let $K=SO(2)$, and let $\Gamma$ be a lattice in $G$, e.g. $SL(2,\mathbb{Z})$...
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2
votes
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Eigenvalues of the imaginary part of the Symplectic action on Siegel upper half plane
Let $A,B\in M_n(\mathbb{R})$ and $U=A+iB$ unitary. $R=diag(r_1,r_2,…,r_n)$ is a diagonal matrix with $r_i>0, \forall i $. I need to calculate $\det(Ae^{-R}A^T+Be^{R}B^T)$. This matrix $Ae^{-R}A^T+...
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2
votes
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250
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characters on unipotent group
Let $G=GL_{n}$ and $N$ the maximal unipotent subgroup, $\mathbb{A}$ the ring of adeles on a number field $F$.
We fix a non trivial character $\psi:F\backslash\mathbb{A}\rightarrow \mathbb{C}^{*}$.
We ...
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1
vote
0
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110
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On continuous part of the L^2 spectrum
Suppose $G$ is a real reductive Lie group and $\Gamma$ is a lattice in $G$ (of finite co-volume). I am reading Langlands's paper " On the functional equation satisfied by the Eisenstein series". I ...
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0
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Holomorphic automorphic/cusp forms on real Lie groups
An automorphic form on a real Lie group $G$ for a discrete subgroup $\Gamma$ is a function $f:G\to\mathbb{C}$ with some properties (see Borel’s definition in Proceedings of Symposia in PURE ...
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