Representation Theory and Complex Analysis: Lectures Given at the C.I.M.E. Summer School Held in Venice, Italy, June 10-17, 2004, 1931. izdevumsSpringer Science & Business Media, 2008. gada 27. febr. - 380 lappuses Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. Michael Cowling presents a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces. Alain Valette recalls the concept of amenability and shows how it is used in the proof of rigidity results for lattices of semisimple Lie groups. Edward Frenkel describes the geometric Langlands correspondence for complex algebraic curves, concentrating on the ramified case where a finite number of regular singular points is allowed. Masaki Kashiwara studies the relationship between the representation theory of real semisimple Lie groups and the geometry of the flag manifolds associated with the corresponding complex algebraic groups. David Vogan deals with the problem of getting unitary representations out of those arising from complex analysis, such as minimal globalizations realized on Dolbeault cohomology with compact support. Nolan Wallach illustrates how representation theory is related to quantum computing, focusing on the study of qubit entanglement. |
Saturs
Applications of Representation Theory to Harmonic Analysis | 1 |
The Equations of Mathematical Physics on Symmetric Spaces | 10 |
The Vanishing of Matrix Coefficients | 22 |
More General Semisimple Groups | 31 |
CarnotCarathéodory Geometry and Group Representations | 38 |
References | 46 |
The Unramified Global Langlands Correspondence | 56 |
Geometric Local Langlands Correspondence over C | 64 |
Integral Transforms | 208 |
Vanishing Theorems | 221 |
References | 229 |
Amenability and Margulis SuperRigidity | 235 |
Margulis Superrigidity Theorem | 252 |
Unitary Representations and Complex Analysis | 259 |
Examples for SL2 R | 272 |
Real Parabolic Induction and the Globalization Functors | 284 |
Center and Opers | 71 |
Opers vs Local Systems | 77 |
Unramified Case | 85 |
Tamely Ramified Case | 99 |
Ramified Global Langlands Correspondence | 117 |
References | 132 |
Derived Categories of Quasiabelian Categories | 152 |
Quasiequivariant DModules | 158 |
Equivariant Derived Category | 176 |
Holomorphic Solution Spaces | 182 |
Whitney Functor | 194 |
Examples of Complex Homogeneous Spaces | 294 |
Dolbeault Cohomology and Maximal Globalizations | 302 |
Compact Supports and Minimal Globalizations | 318 |
Invariant Bilinear Forms and Maps between Representations | 327 |
Open Questions | 341 |
References | 350 |
References | 355 |
References | 362 |
References | 368 |
References | 376 |
Citi izdevumi - Skatīt visu
Representation Theory and Complex Analysis Michael Cowling,Edward Frenkel,Masaki Kashiwara Priekšskatījums nav pieejams - 2008 |