Double Affine Hecke Algebras and Congruence Groups, Bogdan Ion, Siddhartha Sahi

Автор: Kenkichi Iwasawa
Название: Hecke`s L-functions
ISBN: 9811394946 ISBN-13(EAN): 9789811394942
Издательство: Springer
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Описание: This volume contains the notes originally made by Kenkichi Iwasawa in his own handwriting for his lecture course at Princeton University in 1964. These notes give a beautiful and completely detailed account of the adelic approach to Hecke’s L-functions attached to any number field, including the proof of analytic continuation, the functional equation of these L-functions, and the class number formula arising from the Dedekind zeta function for a general number field. This adelic approach was discovered independently by Iwasawa and Tate around 1950 and marked the beginning of the whole modern adelic approach to automorphic forms and L-series. While Tate’s thesis at Princeton in 1950 was finally published in 1967 in the volume Algebraic Number Theory, edited by Cassels and Frohlich, no detailed account of Iwasawa’s work has been published until now, and this volume is intended to fill the gap in the literature of one of the key areas of modern number theory. In the final chapter, Iwasawa elegantly explains some important classical results, such as the distribution of prime ideals and the class number formulae for cyclotomic fields.

Автор: Kazuyuki Hatada
Название: Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms
ISBN: 1470443341 ISBN-13(EAN): 9781470443344
Издательство: Mare Nostrum (Eurospan)
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Описание: The quirky inspiration of the 642 Series takes flight in this collection of fiction-writing prompts that will make anyone want to grab a pen and write what happens next. The prompts in this journal are craftted to offer fully-fledged story ideas, not simply writing exercises, taking the 642 Things to Write About series to new levels of creative amibition and quirkiness.

Автор: Gao Qing
Название: Universal Fuzzy Controllers for Non-Affine Nonlinear Systems
ISBN: 9811094926 ISBN-13(EAN): 9789811094927
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Описание: It presents a number of novel ideas and approaches to various issues including universal function approximation, universal fuzzy models, universal fuzzy stabilization controllers, and universal fuzzy integral sliding mode controllers.

Автор: Nanhua Xi
Название: Representations of Affine Hecke Algebras
ISBN: 3540583890 ISBN-13(EAN): 9783540583899
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Описание: These lecture notes show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. The based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras.

Автор: Maria Chlouveraki
Название: Blocks and Families for Cyclotomic Hecke Algebras
ISBN: 3642030637 ISBN-13(EAN): 9783642030635
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Описание: This book contains a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Cli?ord theory. It can also serve as an introduction to the Hecke algebras of complex re?ection groups. Its aim is the study of the blocks and the determination of the families of characters of the cyclotomic Hecke algebras associated to complex re?ection groups. Iwouldliketothankmythesisadvisor, MichelBrou e, forhisadvice.These Springer Lecture Notes were, after all, his idea. I am grateful to Jean Michel for his help with the implementation and presentation of the programming part. I would like to thank Gunter Malle for his suggestion that I generalize my results on Hecke algebras, which led to the notion of "essential algebras". I also express my thanks to C edric Bonnaf e, Meinolf Geck, Nicolas Jacon, Rapha] el Rouquier and Jacques Th evenaz for their useful comments. Finally, I thank Thanos Tsouanas for copy-editing this manuscript. v Introduction The ?nite groups of matrices with coe?cients in Q generated by re?ections, known as Weyl groups, are a fundamental building block in the classi?cation of semisimple complex Lie algebras and Lie groups, as well as semisimple algebraic groups over arbitrary algebraically closed ?elds. They are also a foundation for many other signi?cant mathematical theories, including braid groups and Hecke algebras.

Автор: Rui Palma
Название: Crossed Products by Hecke Pairs
ISBN: 1470428091 ISBN-13(EAN): 9781470428099
Издательство: Mare Nostrum (Eurospan)
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Описание: Develops a theory of crossed products by actions of Hecke pairs $(G, \Gamma )$, motivated by applications in non-abelian $C^*$-duality. The author`s approach gives back the usual crossed product construction whenever $G / \Gamma $ is a group and retains many of the aspects of crossed products by groups.

Автор: Chun-Ju Lai, Li Luo, Weiqiang Wang, Yiqiang Li, Zhaobing Fan
Название: Affine Flag Varieties and Quantum Symmetric Pairs
ISBN: 1470441756 ISBN-13(EAN): 9781470441753
Издательство: Mare Nostrum (Eurospan)
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Описание: Demonstrates that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine $\mathfrak{sl}$ and $\mathfrak{gl}$ types, respectively. In this way, the authors provide geometric realizations of eight quantum symmetric pairs of affine types.

Автор: Kuroda Shigeru, Onoda Nobuharu, Freudenburg Gene
Название: Polynomial Rings and Affine Algebraic Geometry: Praag 2018, Tokyo, Japan, February 12-16
ISBN: 303042135X ISBN-13(EAN): 9783030421359
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Описание: This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018.

Автор: Eduardo Garcia-Rio, Peter Gilkey, Stana Nik?evi?, Ramon Vazquez-Lorenzo
Название: Applications of Affine and Weyl Geometry
ISBN: 1608457591 ISBN-13(EAN): 9781608457595
Издательство: Mare Nostrum (Eurospan)
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Описание: Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need-proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting.The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possible to find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.

Автор: Yorck Sommerhauser, Yongchang Zhu
Название: Hopf Algebras and Congruence Subgroups
ISBN: 0821869132 ISBN-13(EAN): 9780821869130
Издательство: Mare Nostrum (Eurospan)
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Описание: "September 2012, volume 219, number 1028 (first of 5 numbers)."

Автор: Ceccherini-Silberstein Tullio, Scarabotti Fabio, Tolli Filippo
Название: Gelfand Triples and Their Hecke Algebras: Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups
ISBN: 3030516067 ISBN-13(EAN): 9783030516062
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Описание: This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs.

Автор: Dra?en Adamovi?; Paolo Papi
Название: Affine, Vertex and W-algebras
ISBN: 3030329054 ISBN-13(EAN): 9783030329051
Издательство: Springer
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Описание: This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.