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Elements of the Representation Theory of the Jacobi Group

2013-11-09 Mathematics
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Release : 2013-11-09
Genre : Mathematics
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Book Rating : 728/5 ( reviews)

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Book Synopsis Elements of the Representation Theory of the Jacobi Group by : Rolf Berndt

Download or read book Elements of the Representation Theory of the Jacobi Group written by Rolf Berndt. This book was released on 2013-11-09. Available in PDF, EPUB and Kindle. Book excerpt: The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.

Elements of the Representation Theory of the Jacobi Group

2012-01-05 Mathematics
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Release : 2012-01-05
Genre : Mathematics
Kind : eBook
Book Rating : 82X/5 ( reviews)

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Book Synopsis Elements of the Representation Theory of the Jacobi Group by : Rolf Berndt

Download or read book Elements of the Representation Theory of the Jacobi Group written by Rolf Berndt. This book was released on 2012-01-05. Available in PDF, EPUB and Kindle. Book excerpt: Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.

Elements of the Representation Theory of the Jacobi Group

1997
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Release : 1997
Genre :
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Book Synopsis Elements of the Representation Theory of the Jacobi Group by : Rolf Berndt

Download or read book Elements of the Representation Theory of the Jacobi Group written by Rolf Berndt. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt:

Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields

2014-12-05 Mathematics
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Release : 2014-12-05
Genre : Mathematics
Kind : eBook
Book Rating : 163/5 ( reviews)

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Book Synopsis Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields by : Hatice Boylan

Download or read book Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields written by Hatice Boylan. This book was released on 2014-12-05. Available in PDF, EPUB and Kindle. Book excerpt: The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory of Jacobi forms over the rational numbers, which is an indispensable tool in the arithmetic theory of elliptic modular forms, elliptic curves, and in many other disciplines in mathematics and physics. Jacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite quadratic modules and associated Weil representations over number fields. This part might also be interesting for those who are merely interested in the representation theory of Hilbert modular groups. One of the main applications is the complete classification of Jacobi forms of singular weight over an arbitrary totally real number field.

Introduction to Representation Theory

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 511/5 ( reviews)

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Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof

Download or read book Introduction to Representation Theory written by Pavel I. Etingof. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

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