Representation Theory and Complex Analysis

Lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004

Enrico Casadio Tarabusi, Andrea D'Agnolo, Massimo A. Picardello (Herausgeber)

Michael Cowling, Edward Frenkel, Masaki Kashiwara, Alain Valette, David A. Vogan, Nolan R. Wallach (Autoren)

Buch | Softcover

XII, 389 Seiten

2008 | 2008
Springer Berlin (Verlag)
978-3-540-76891-3 (ISBN)

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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.

Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa).- Ramifications of the Geometric Langlands Program.- Equivariant Derived Category and Representation of Real Semisimple Lie Groups.- Amenability and Margulis Super-Rigidity.- Unitary Representations and Complex Analysis.- Quantum Computing and Entanglement for Mathematicians.

Erscheint lt. Verlag	27.2.2008
Reihe/Serie	Lecture Notes in Mathematics ; 1931
Zusatzinfo	XII, 389 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	22EXX, 43AXX, 17BXX, 58GXX, 81P68 • Abstract harmonic analysis • Complex Analysis • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • Harmonic Analysis • HC/Mathematik/Arithmetik, Algebra • Langlands correspondence • quasi-equivariant D-modules • Representation Theory • semisimple Lie groups • unitary representations
ISBN-10	3-540-76891-2 / 3540768912
ISBN-13	978-3-540-76891-3 / 9783540768913
Zustand	Neuware