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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.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 693. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- General introduction I. General theory 1. The formal completions of $G(A)$ and $G(A)/B$ 2. Measures on the formal flag space II. Infinite classical groups 0. Introduction for Part II 1. Measures on the formal flag space 2. The case $\mathfrak {g} = sl(\infty, \mathbb {C})$ 3. The case $\mathfrak {g} = sl(2\infty, \mathbb {C})$ 4. The cases $\mathfrak {g} = o(2\infty, \mathbb {C})$, $o(2\infty + 1, \mathbb {C})$, and $sp(\infty, \mathbb {C})$ III. Loop groups 0. Introduction for Part III 1. Extensions of loop groups 2. Completions of loop groups 3. Existence of the measures $\nu _{\beta, k}$, $\beta> 0$ 4. Existence of invariant measures IV. Diffeomorphisms of $S^1$ 0. Introduction for Part IV 1. Completions and classical analysis 2. The extension $\hat {\mathcal {D}}$ and determinant formulas 3. The measures $\nu _{\beta, c, h}$, $\beta> 0$, $c, h \geq 0$ 4. On existence of invariant measures.