The Orbit Method in Geometry and Physics: In Honor of A.A. Kirillov

ISBN-13: 9781461265801 / Angielski / Miękka / 2013 / 474 str.

Christian Duval; Laurent Guieu; Valentin Ovsienko

Opis

The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

Recenzje

"...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.

Spis treści

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 * Gerbes of Chiral Differential Operators. III * Defining Relations for the Exceptional Superalgebras of Vector Fields * Schur-Weyl Duality and Representations of Permutation Groups * Quantiziation of Hypersurface Orbitla Varieties in sln * 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 of GLn(C) at Infinity: Hinges, Complete Collineations, Projective Compactifications, and Universal Boundary * 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

O autorze

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.