Symmetric Spaces and the Kashiwara-Vergne Method (Lecture by François Rouvière

By François Rouvière

accumulating and updating effects scattered in magazine articles over thirty years, this self-contained monograph offers a entire advent to the topic. Its objective is to: - inspire and clarify the strategy for common Lie teams, decreasing the facts of deep ends up in invariant research to the verification of 2 formal Lie bracket identities concerning the Campbell-Hausdorff formulation (the "Kashiwara-Vergne conjecture"); - supply a close evidence of the conjecture for quadratic and solvable Lie algebras, that's really common; - expand the strategy to symmetric areas; the following an obstruction looks, embodied in one notable item known as an "e-function"; - clarify the function of this functionality in invariant research on symmetric areas, its relation to invariant differential operators, suggest price operators and round services; - provide an specific e-function for rank one areas (the hyperbolic spaces); - build an e-function for basic symmetric areas, within the spirit of Kashiwara and Vergne's unique paintings for Lie teams. The publication incorporates a entire rewriting of numerous articles via the writer, up-to-date and stronger following Alekseev, Meinrenken and Torossian's fresh proofs of the conjecture. The chapters are principally self reliant of one another. a few open difficulties are prompt to inspire destiny study. it really is aimed toward graduate scholars and researchers with a easy wisdom of Lie theory.

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