Equivariant Analytic Localization Of Group Representations

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Equivariant Analytic Localization Of Group Representations

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Author : Laura Ann Smithies
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Equivariant Analytic Localization Of Group Representations written by Laura Ann Smithies and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

This book is intended for graduate students and research mathematicians interested in topological groups, Lie groups, category theory, and homological algebra.

From Representation Theory To Homotopy Groups

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Author : Donald M. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

From Representation Theory To Homotopy Groups written by Donald M. Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applys this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989.

Equivariant Orthogonal Spectra And S Modules

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Author : M. A. Mandell
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Equivariant Orthogonal Spectra And S Modules written by M. A. Mandell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The last few years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993. The most well-known examples are the category of $S$-modules and the category of symmetric spectra. We focus on the category of orthogonal spectra, which enjoys some of the best features of $S$-modules and symmetric spectra and which is particularly well-suited to equivariant generalization. We first complete the nonequivariant theory by comparing orthogonal spectra to $S$-modules. We then develop the equivariant theory.For a compact Lie group $G$, we construct a symmetric monoidal model category of orthogonal $G$-spectra whose homotopy category is equivalent to the classical stable homotopy category of $G$-spectra. We also complete the theory of $S_G$-modules and compare the categories of orthogonal $G$-spectra and $S_G$-modules. A key feature is the analysis of change of universe, change of group, fixed point, and orbit functors in these two highly structured categories for the study of equivariant stable homotopy theory.

Representation Theory And Complex Analysis

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Author : Michael Cowling
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-27

Representation Theory And Complex Analysis written by Michael Cowling and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-27 with Mathematics categories.

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.

The Ab Program In Geometric Analysis Sharp Sobolev Inequalities And Related Problems

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Author : Olivier Druet
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

The Ab Program In Geometric Analysis Sharp Sobolev Inequalities And Related Problems written by Olivier Druet and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.

The Submanifold Geometries Associated To Grassmannian Systems

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Author : Martina Brück
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

The Submanifold Geometries Associated To Grassmannian Systems written by Martina Brück and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.

Several Complex Variables With Connections To Algebraic Geometry And Lie Groups

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Author : Joseph L. Taylor
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-21

Several Complex Variables With Connections To Algebraic Geometry And Lie Groups written by Joseph L. Taylor and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-21 with Mathematics categories.

This text presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraic sheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest are the last three chapters, which are devoted to applications of the preceding material to the study of the structure and representations of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Mili?i?'s proof of the Borel-Weil-Bott theorem, which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for the expert.

Numerical Control Over Complex Analytic Singularities

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Author : David B. Massey
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Numerical Control Over Complex Analytic Singularities written by David B. Massey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Generalizes the Le cycles and numbers to the case of hyper surfaces inside arbitrary analytic spaces. This book defines the Le-Vogel cycles and numbers, and prove that the Le-Vogel numbers control Thom's $a_f$ condition. It describes the relationship between the Euler characteristic of the Milnor fibre and the Le-Vogel numbers.

The Based Ring Of Two Sided Cells Of Affine Weyl Groups Of Type Widetilde A N 1

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Author : Nanhua Xi
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

The Based Ring Of Two Sided Cells Of Affine Weyl Groups Of Type Widetilde A N 1 written by Nanhua Xi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.

Noether Lefschetz Problems For Degeneracy Loci

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Author : Jeroen Spandaw
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Noether Lefschetz Problems For Degeneracy Loci written by Jeroen Spandaw and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Studies the cohomology of degeneracy loci. This title assumes that $E\otimes F DEGREES\vee$ is ample and globally generated, and that $\psi$ is a general homomorphism. In order to study the cohomology of $Z$, it considers the Grassmannian bundle $\pi\colon Y: =\mathbb{G}(f-r, F)\to X$ of $(f-r)$-dimensional linear subspaces of the fibre