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This volume contains a series of lectures presented at the 2nd Session of the Centro Internazionale Matematica Estivo (CIME), held in Venezia, Italy in June 1992. It includes discussion of quantum groups and the index theorems for R-constructible sheaves and for D-modules. CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.
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