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Invariant measures for unitary groups associated to Kac-Moody Lie algebras /
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 meas...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
©2000.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 693. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Pickrell, Doug, |d 1952- |1 https://id.oclc.org/worldcat/entity/E39PCjB7Y3RYfg4td7Rw8HHPV3 | |
| 245 | 1 | 0 | |a Invariant measures for unitary groups associated to Kac-Moody Lie algebras / |c Doug Pickrell. |
| 260 | |a Providence, R.I. : |b American Mathematical Society, |c ©2000. | ||
| 300 | |a 1 online resource (ix, 125 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 1947-6221 ; |v v. 693 | |
| 500 | |a "July 2000, volume 146, number 693 (second of 5 numbers)." | ||
| 504 | |a Includes bibliographical references (pages 123-125). | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a 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 | |
| 505 | 0 | 0 | |t General introduction |t I. General theory |t 1. The formal completions of $G(A)$ and $G(A)/B$ |t 2. Measures on the formal flag space |t II. Infinite classical groups |t 0. Introduction for Part II |t 1. Measures on the formal flag space |t 2. The case $\mathfrak {g} = sl(\infty, \mathbb {C})$ |t 3. The case $\mathfrak {g} = sl(2\infty, \mathbb {C})$ |t 4. The cases $\mathfrak {g} = o(2\infty, \mathbb {C})$, $o(2\infty + 1, \mathbb {C})$, and $sp(\infty, \mathbb {C})$ |t III. Loop groups |t 0. Introduction for Part III |t 1. Extensions of loop groups |t 2. Completions of loop groups |t 3. Existence of the measures $\nu _{\beta, k}$, $\beta> 0$ |t 4. Existence of invariant measures |t IV. Diffeomorphisms of $S^1$ |t 0. Introduction for Part IV |t 1. Completions and classical analysis |t 2. The extension $\hat {\mathcal {D}}$ and determinant formulas |t 3. The measures $\nu _{\beta, c, h}$, $\beta> 0$, $c, h \geq 0$ |t 4. On existence of invariant measures. |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Kac-Moody algebras. | |
| 650 | 0 | |a Invariant measures. | |
| 650 | 0 | |a Unitary groups. | |
| 650 | 6 | |a Algèbres de Kac-Moody. | |
| 650 | 6 | |a Mesures invariantes. | |
| 650 | 6 | |a Groupes unitaires. | |
| 650 | 7 | |a Invariant measures |2 fast | |
| 650 | 7 | |a Kac-Moody algebras |2 fast | |
| 650 | 7 | |a Unitary groups |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Pickrell, Doug, 1952- |t Invariant measures for unitary groups associated to Kac-Moody Lie algebras / |x 0065-9266 |z 9780821820681 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 693. |x 0065-9266 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114469 |z Texto completo |
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