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Smooth-Automorphic Forms and Smooth-Automorphic Representations

2021
This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider "K-finite" automorphic forms, but we allow a richer class ...
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Construction of automorphic Galois representations: the self-dual case

Shimura Varieties, 2020
This survey paper grew out of the author’s lecture notes for the Clay Summer School in 2009. Proofs are often omitted or sketched, but a number of references are given to help the reader find more details if he or she wishes.
Woo Shin Sug
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Dimensions of Automorphic Representations, L-Functions and Liftings

, 2019
There are many Rankin-Selberg integrals representing Langlands $L$-functions, and it is not apparent what the limits of the Rankin-Selberg method are.
S. Friedberg, D. Ginzburg
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GEOMETRIC CYCLES IN COMPACT LOCALLY HERMITIAN SYMMETRIC SPACES AND AUTOMORPHIC REPRESENTATIONS

Transformation groups, 2017
Let G be a linear connected non-compact real simple Lie group and let K ⊂ G be a maximal compact subgroup of G. Suppose that the centre of K is isomorphic to 𝕊1 so that X := G/K is a global Hermitian symmetric space.
Arghya Mondal, P. Sankaran
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Semistable representations of quivers with automorphism

Science China Mathematics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Global rigid inner forms and multiplicities of discrete automorphic representations

, 2015
We study the cohomology of certain Galois gerbes over number fields. This cohomology provides a bridge between refined local endoscopy, as introduced in Kaletha (Ann Math (2) 184(2):559–632, 2016), and classical global endoscopy.
Tasho Kaletha
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Continuity of automorphic representations

Mathematical Proceedings of the Cambridge Philosophical Society, 1973
Let ℛ be a von Neumann algebra, with predual ℛ*, acting on a Hilbert space ℋ; G a locally compact group with left Haar measure m, and α a representation of G on aut (ℛ), the group of all *-automorphisms of ℛ, i.e. α is a group homomorphism from G to aut (ℛ).
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Selberg’s integral for Ramanujan automorphic representation

Acta Mathematica Sinica, English Series, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Representations of Inverse Monoids by Partial Automorphisms

SemiGroup Forum, 2000
A category \(\mathbf C\) is \((E,M)\)-structured if it has subcategories \(E\) and \(M\) such that (1) \(\text{Iso}({\mathbf C})\subseteq E\cap M\) and (2) each morphism \(f\) may be factored as \(f=em\) where \(e\in E\) and \(m\in M\) and if \(e_1m_1=f=e_2m_2\), then \(e_1=e_2u\) and \(um_1=m_2\) for a unique isomorphism \(u\). An \((E,M)\)-structured
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Equivariant Polynomial Automorphisms Of Θ-Representations

Canadian Journal of Mathematics, 1998
AbstractWe show that every equivariant polynomial automorphism of a Θ- representation and of the reduction of an irreducible Θ-representation is a multiple of the identity.
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