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

Includes bibliographical references (p. 123-125).

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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