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11 votes
0 answers
283 views

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 ...
Daniel Miller's user avatar
9 votes
1 answer
639 views

Borel's Paris Lectures

I am trying to read Harish-Chandra's book on automorphic forms on Semisimple Lie groups, and he keeps referring to Borel's Paris lecture notes. Does anyone have an online version of these notes or ...
admissiblecycle's user avatar
8 votes
1 answer
1k views

Multiplicity one theorem

I am reading Dorian Goldfeld's book Automorphic forms and L functions for the groups GL(n,R) (http://www.cambridge.org/us/academic/subjects/mathematics/number-theory/automorphic-forms-and-l-functions-...
Wiener Schmidt's user avatar
6 votes
1 answer
551 views

Two definitions of automorphic forms on Lie groups

My question is the about the equivalence of two definitions of automorphic forms on a semisimple Lie group. The most common definition of automorphic forms on a semisimple Lie group $G$ with respect ...
Jun Yang's user avatar
  • 391
6 votes
1 answer
765 views

What is a map for the representation theory of reductive groups?

I have finished learning about linear algebraic groups (minus their representation theory) and the associated algebraic structures (root data, root systems, etc.), and will next attempt to summarize ...
Andrew NC's user avatar
  • 2,071
0 votes
0 answers
159 views

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 ...
Jun Yang's user avatar
  • 391