Invariant measures for unitary groups associated to Kac-Moody Lie algebras / Doug Pickrell.

Format:

Book

Author/Creator:

Pickrell, Doug, 1952- author.

Series:

Memoirs of the American Mathematical Society ; no. 693.

Memoirs of the American Mathematical Society, 0065-9266 ; number 693

Language:

English

Subjects (All):

Kac-Moody algebras.

Invariant measures.

Unitary groups.

Physical Description:

1 online resource (143 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2000]

Language Note:

English

Summary:

The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other "invariant measures" are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.

Contents:

Intro

Contents

General Introduction

Part I. General Theory

Chapter 1. The Formal Completions of G(A) and G(A)/B

Chapter 2. Measures on the Formal Flag Space

Part II. Infinite Classical Groups

Chapter 0. Introduction for Part II

Chapter 1. Measures on the Formal Flag Space

Chapter 2. The Case g = sl(∞, C)

Chapter 3. The Case g = sl(2∞, C)

Chapter 4. The Cases g = o(2∞, C), o(2∞+1, C), sp(∞, C)

Part III. Loop Groups

Chapter 0. Introduction for Part III

Chapter 1. Extensions of Loop Groups

Chapter 2. Completions of Loop Groups

Chapter 3. Existence of the Measures V[sub(β,k)], β&gt

0

Chapter 4. Existence of Invariant Measures

Part IV. Diffeomorphisms of S[sup(1)]

Chapter 0. Introduction for Part IV

Chapter 1. Completions and Classical Analysis

Chapter 2. The extension D and determinant formulas

Chapter 3. The measures V[sub(β,c,h)], β&gt

0, c,h≥0

Chapter 4. On Existence of Invariant Measures

Concluding Comments

Acknowledgements

References.

Notes:

"July 2000, volume 146, number 693 (second of 5 numbers)."

Includes bibliographical references (pages 123-125).

Description based on print version record.

ISBN:

1-4704-0284-X