The Orbit Method in Geometry and Physics - Christian Duval

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Résumé :
A.A. Kirillov's pioneering 1962 paper on nilpotent orbits places him as the founder of orbit theory. The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and continues to be an important tool today. In this volume, prominent contributors present original and expository invited papers in the areas of Lie theory, geometry, algebra, and mathematical physics. An invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses....

Sommaire:
A Principle of Variations in Representation Theory.- Finite Group Actions on Poisson Algebras.- Representations of Quantum Tori and G-bundles on Elliptic Curves.- Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I.- Br?ves remarques sur l'oeuvre de A. A. Kirillov.- Gerbes of Chiral Differential Operators. III.- Defining Relations for the Exceptional Lie Superalgebras of Vector Fields.- Schur-Weyl Duality and Representations of Permutation Groups.- Quantization of Hypersurface Orbital Varieties insln.- Generalization of a Theorem of Waldspurger to Nice Representations.- Two More Variations on the Triangular Theme.- The Generalized Cayley Map from an Algebraic Group to its Lie Algebra.- Geometry ofGLn(?)at Infinity: Hinges, Complete Collineations, Projective Compactifications, and Universal Boundary.- Why Would Multiplicities be Log-Concave?.- Point Processes Related to the Infinite Symmetric Group.- Some Toric Manifolds and a Path Integral.- Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces.- Maximal Subalgebras of the Classical Linear Lie Superalgebras.

...the volume might be useful to a large number of potential readers interested in various fields, like representation theory of Lie groups, symplectic geometry, differential equations, combinatorics, etc. It is noteworthy that the history of mathematics can also be added to this list of topics, due to the nice article authored by J. Dixmier. -Romanian Journal of Pure and Appl. Math.