Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras.

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.

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