4 edition of **Representations of real reductive lie groups** found in the catalog.

Representations of real reductive lie groups

AMS-IMS-SIAM Joint Summer Research Conference (2006 Snowbird, Utalh)

- 162 Want to read
- 28 Currently reading

Published
**2008**
by American Mathematical Society in Providence, R.I
.

Written in English

- Representations of Lie groups -- Congresses

**Edition Notes**

Includes bibliographical references.

Statement | James Arthur, Wilfried Schmid, Peter E. Trapa, editors. |

Genre | Congresses. |

Series | Contemporary mathematics -- v. 472 |

Contributions | Arthur, James, 1944-, Schmid, Wilfried, 1943-, Trapa, Peter E., 1974- |

Classifications | |
---|---|

LC Classifications | QA387 .A446 2006 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL16900848M |

ISBN 10 | 9780821843666 |

LC Control Number | 2008024593 |

Varadarajan, Unitary Representations of Super Lie Groups (free) Wallach, Representations of Reductive Lie Groups (free) Books on Lie Groups, Representations. Atiyah et al, Representation Theory of Lie Groups (unfree) Brocker, tom Dieck, Representations of Compact Lie Groups (unfree) Gelfand (ed.), Lie Groups and their Representations (unfree). Suppose G is a real reductive Lie group in Harish-Chandra’s class (see [6, §3]). We propose here a structure for the set Πu(G) of equivalence classes of irreducibleunitary representations of G. (The subscriptu will be used through-out to indicate structures related to unitary representations.

These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their cat-egories of representations. Eventually these notes will consist of three chapters, each about pages long, and a short appendix. BibTeX information: @misc{milneLAG. Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting.

Publisher Summary. This chapter discusses irreducibility of discrete series representations for semi-simple symmetric spaces. It explains the term translation principle that refers to the idea of studying infinite dimensional representations of reductive Lie algebras by investigating their tensor products with the rich, complicated, and well-understood family of finite-dimensional. Relative Lie algebra cohomology and unitary representations of complex Lie groups. Thomas J. Enright Continuous cohomology and unitary representations of real reductive groups, Ann. of Math. (2) (), no. 3, Wave front sets of reductive Lie group representations Harris, Benjamin, He, Hongyu, and Ólafsson.

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Buy Representations of Real Reductive Lie Groups (Progress in Mathematics) on FREE SHIPPING on qualified orders Representations of Real Reductive Lie Groups (Progress in Mathematics): Vogan, David A.: : Books. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on MayThis volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored.

Representations of Real Reductive Lie Groups Volume 15 of Progress in Mathematics - Birkhäuser, ISSN Volume 15 of Progress in mathematics, ISSN Author: David A. Vogan: Publisher: Birkhaüser Boston, Original from: the University of California: Digitized: ISBN:Length: Additional Physical Format: Online version: Vogan, David A., Representations of real reductive Lie groups.

Cambridge, Mass.: Birkhäuser Boston, Unitary Representations of Reductive Lie Groups. This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs.

The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference “Representation Theory of Real Reductive Lie Groups” held in Snowbird, Utah in Junewith the aim of elucidating the problems that remain, as well as explaining what tools have.

Localization and Representation Theory of Reductive Lie Groups Dragan Mili ci c. Contents Chapter 1. Sheaves of di erential operators 1 1. Twisted sheaves of di erential operators 1 Group actions on ag varieties 85 2. Harish-Chandra pairs 86 3. Harish-Chandra modules and Harish-Chandra sheaves 87 4.

The n-homology of Harish-Chandra modules \Representation theory of semisimple groups" and here is a summary of what I learnt so far. Warning: these notes get vaguer/sloppier as they go on.

1 Reductive Lie algebras over R. Let g be a real Lie algebra with the property that g C:= g R C is reductive in the usual sense of complex Lie algebras. Lecture 1 Representations of reductive Lie groups notes is an object that is both a group and a di erentiable manifold.

You can carry out the same constructions in the category of complex manifolds. To even de ne a complex manifold, technically, you need to know what a holomorphic function in several complex variables is. I am interested in any sources that can be helpful for learning the representation theory of real reductive groups.

I am currently reading Wallach book, but I feel that I don't understand the subject properly and want to find an alternative. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs.

The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction.

This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups.

The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the yearspecifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands.

This course gives an introduction to in nite-dimensional representations of real reductive Lie groups such as GL(n;R) by geometric and analytic meth-ods. I begin with some basic concepts and techniques on real reductive Lie groups, their representations, and global analysis via representation theory, with a number of classical examples.

WAVE FRONT SETS OF REDUCTIVE LIE GROUP REPRESENTATIONS 3 Theorem If Gis a reductive Lie group of Harish-Chandra class and ˇ is weakly contained in the regular representation of G, then SS(ˇ) = WF(ˇ) = AC(O-suppˇ): When Gis compact and connected, an equivalent formula for SS(ˇ) was obtained by Kashiwara and Vergne in Corollary of.

Representations of Lie Groups The course is about irreducible unitary representations of a real reductive Lie group G. I want to describe an algorithm to classify these representations. Here is the setting.

A representation of G is an action of G by linear operators on. COMPLEX GEOMETRY AND REPRESENTATIONS OF LIE GROUPS 0. Introduction. There is an mysterious intimate correlation between the theory of homogeneous complex manifolds and the theory of unitary representations of real Lie groups.

This relation is becoming clear in the case of a real reductive Lie group Go. Let G be. Combinatorics for the representation theory of real reductive groups Fokko du Cloux Aug These are notes for the third meeting of the Atlas of reductive Lie groups project at AIM, in Palo Alto.

They describe how to take the description of the representation theory of a real reductive Lie group. Unitary Representations of Reductive Lie Groups.

(AM), Volume This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January special unitary representations of Levi subgroups. Introduction Suppose G is a real reductive Lie group in Harish-Chandra’s class (see [HC], section 3).

There are two powerful general techniques for con-structing irreducible unitary representations of G. Parabolic induction is based on real analysis and geometry on certain compact. Representations of Real Reductive Lie Groups (Introduction and Chapter 1). The topic of this book is the construction and classification of all irreducible representations of real reductive Lie groups, using ideas introduced by Zuckerman in the late s.

The topic of Chapter 1 is the special case of SL(2,R). For general groups there are more serious di culties, described by von Neumann’s theory of \types." But one of Harish-Chandra’s fundamental theorems ([9], Theorem 7) is that real reductive Lie groups are \type I," and therefore that any unitary representation of a reductive group may.Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations.

Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful Cited by: Based on the "Hermann Weyl Lectures" given at the Institute for Advanced Study in January This title outlines some of what is known about irreducible unitary representations of real reductive .