简介
Summary:
Publisher Summary 1
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.
目录
Table Of Contents:
Preface vii
A Principle of Variations in Representation Theory 1(8)
A. Alekseev
F. Petrov
Finite Group Actions on Poisson Algebras 9(20)
Jacques Alev
Daniel R. Farkas
Representations of Quantum Tori and G-bundles on Elliptic Curves 29(20)
Vladimir Baranovsky
Sam Evens
Victor Ginzburg
Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft--Procesi Models I 49(20)
Ranee Brylinski
Breves remarques sur l'oeuvre de A. A. Kirillov 69(4)
Jacques Dixmier
Gerbes of Chiral Differential Operators. III 73(28)
Vassily Gorbounov
Fyodor Malikov
Vadim Schechtman
Defining Relations for the Exceptional Lie Superalgebras of Vector Fields 101(46)
Pavel Grozman
Dimitry Leites
Irina Shchepochkina
Schur--Weyl Duality and Representations of Permutation Groups 147(18)
Eugene Gutkin
Quantization of Hypersurface Orbital Varieties in sln 165(32)
Anthony Joseph
Anna Melnikov
Generalization of a Theorem of Waldspurger to Nice Representations 197(46)
D. Kazhdan
A. Polischuk
Two More Variations on the Triangular Theme 243(16)
A. A. Kirillov
The Generalized Cayley Map from an Algebraic Group to its Lie Algebra 259(38)
Bertram Kostant
Peter W. Michor
Geometry of GLn(C) at Infinity: Hinges, Complete Collineations, Projective Compactifications, and Universal Boundary 297(32)
Yurii A. Neretin
Why Would Multiplicities be Log-Concave? 329(20)
Andrei Okounkov
Point Processes Related to the Infinite Symmetric Group 349(46)
Grigori Olshanski
Some Toric Manifolds and a Path Integral 395(26)
W. Rossmann
Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces 421(24)
Alexander Sergeev
Maximal Subalgebras of the Classical Linear Lie Superalgebras 445
Irina Shchepochkina
Preface vii
A Principle of Variations in Representation Theory 1(8)
A. Alekseev
F. Petrov
Finite Group Actions on Poisson Algebras 9(20)
Jacques Alev
Daniel R. Farkas
Representations of Quantum Tori and G-bundles on Elliptic Curves 29(20)
Vladimir Baranovsky
Sam Evens
Victor Ginzburg
Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft--Procesi Models I 49(20)
Ranee Brylinski
Breves remarques sur l'oeuvre de A. A. Kirillov 69(4)
Jacques Dixmier
Gerbes of Chiral Differential Operators. III 73(28)
Vassily Gorbounov
Fyodor Malikov
Vadim Schechtman
Defining Relations for the Exceptional Lie Superalgebras of Vector Fields 101(46)
Pavel Grozman
Dimitry Leites
Irina Shchepochkina
Schur--Weyl Duality and Representations of Permutation Groups 147(18)
Eugene Gutkin
Quantization of Hypersurface Orbital Varieties in sln 165(32)
Anthony Joseph
Anna Melnikov
Generalization of a Theorem of Waldspurger to Nice Representations 197(46)
D. Kazhdan
A. Polischuk
Two More Variations on the Triangular Theme 243(16)
A. A. Kirillov
The Generalized Cayley Map from an Algebraic Group to its Lie Algebra 259(38)
Bertram Kostant
Peter W. Michor
Geometry of GLn(C) at Infinity: Hinges, Complete Collineations, Projective Compactifications, and Universal Boundary 297(32)
Yurii A. Neretin
Why Would Multiplicities be Log-Concave? 329(20)
Andrei Okounkov
Point Processes Related to the Infinite Symmetric Group 349(46)
Grigori Olshanski
Some Toric Manifolds and a Path Integral 395(26)
W. Rossmann
Projective Schur Functions as Bispherical Functions on Certain Homogeneous Superspaces 421(24)
Alexander Sergeev
Maximal Subalgebras of the Classical Linear Lie Superalgebras 445
Irina Shchepochkina
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