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Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character

2010 Mathematics
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Release : 2010
Genre : Mathematics
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Book Rating : 224/5 ( reviews)

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Book Synopsis Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character by : Ping-Shun Chan

Download or read book Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character written by Ping-Shun Chan. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 204, number 957 (first of 5 numbers)."

Invariant Representations of GSp(2)

2005 Automorphic forms
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Release : 2005
Genre : Automorphic forms
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Book Synopsis Invariant Representations of GSp(2) by : Ping-Shun Chan

Download or read book Invariant Representations of GSp(2) written by Ping-Shun Chan. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Let F be a number field or a p-adic field. We introduce in Chapter 2 of this work two reductive rank one F-groups, H1, H2, which are twisted endoscopic groups of GSp(2) with respect to a fixed quadratic character [epsilon] of the idèle class group of F if F is global, F[superscript X] if F is local. If F is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of H1, H2 to those of GSp(2). In Chapter 4, we establish this lifting in terms of the Satake parameters which parametrize the automorphic representations. By means of this lifting we provide a classification of the discrete spectrum automorphic representations of GSp(2) which are invariant under tensor product with [epsilon]. The techniques through which we arrive at our results are inspired by those of Kazhdan's in [K]. In particular, they involve comparing the spectral sides of the trace formulas for the groups under consideration. We make use of the twisted extension of Arthur's trace formula, and Kottwitz-Shelstad's stabilization of the elliptic component of the geometric side of the twisted trace formula. If F is local, in Chapter 5 we provide a classification of the irreducible admissible representations of GSp(2, F) which are invariant under tensor product with the quadratic character [epsilon] of F[superscript X]. Here, our techniques are also directly inspired by [K]. More precisely, we use the global results from Chapter 4 to express the twisted characters of these invariant representations in terms of the characters of the admissible representations of H[subscript i](F) (i = 1, 2). These (twisted) character identities provide candidates for the liftings predicted by the local component of the conjectural Langlands functoriality. The proofs rely on Sally-Tadić's classification of the irreducible admissible representations of GSp(2, F), and Flicker's results on the lifting from PGSp(2) to PGL(4).

Automorphic Forms and Even Unimodular Lattices

2019-02-28 Mathematics
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Release : 2019-02-28
Genre : Mathematics
Kind : eBook
Book Rating : 917/5 ( reviews)

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Book Synopsis Automorphic Forms and Even Unimodular Lattices by : Gaëtan Chenevier

Download or read book Automorphic Forms and Even Unimodular Lattices written by Gaëtan Chenevier. This book was released on 2019-02-28. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.

Spectral Graph Theory

1997 Mathematics
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Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : 158/5 ( reviews)

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Book Synopsis Spectral Graph Theory by : Fan R. K. Chung

Download or read book Spectral Graph Theory written by Fan R. K. Chung. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses spectral graph theory.

Automorphic Forms

2014-11-19 Mathematics
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Release : 2014-11-19
Genre : Mathematics
Kind : eBook
Book Rating : 526/5 ( reviews)

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Book Synopsis Automorphic Forms by : Bernhard Heim

Download or read book Automorphic Forms written by Bernhard Heim. This book was released on 2014-11-19. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.

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