Functional Analysis on the Eve of the 21st Century

1. Front Matter

   Pages i-xxiii

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2. Connection formulas in the q-analog de Rham cohomology

   • Kazuhiko Aomoto

   Pages 1-12

3. Lagrangian Models of Minimal Representations of E ₆ E ₇ and E ₈

   • Ranee Brylinski, Bertram Kostant

   Pages 13-63

4. Trigonometric Solutions of the Yang-Baxter Equation, Nets, and Hypergeometric Functions

   • Igor B. Frenkel, Vladimir G. Turaev

   Pages 65-118

5. Analogies between the Langlands Correspondence and Topological Quantum Field Theory

   • M. M. Kapranov

   Pages 119-151

6. “Forms” of the Principal Series for GL _n

   • David Kazhdan

   Pages 153-171

7. Geometry of determinants of elliptic operators

   • Maxim Kontsevich, Simeon Vishik

   Pages 173-197

8. Quantum groups at v = ∞

   • George Lusztig

   Pages 199-221

9. The Symplectic Operad

   • Olivier Mathieu

   Pages 223-243

10. Quadratic unipotent representations of p-adic groups

    • C. Moeglin

    Pages 245-262

11. On the Master Field in Two Dimensions

    • I. M. Singer

    Pages 263-281

12. Physical Methods Applied to Donaldson Theory

    • Edward Witten

    Pages 283-292

13. Back Matter

    Pages 293-296

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A four-day conference, "Functional Analysis on the Eve of the Twenty­ First Century," was held at Rutgers University, New Brunswick, New Jersey, from October 24 to 27, 1993, in honor of the eightieth birthday of Professor Israel Moiseyevich Gelfand. He was born in Krasnye Okna, near Odessa, on September 2, 1913. Israel Gelfand has played a crucial role in the development of functional analysis during the last half-century. His work and his philosophy have in fact helped to shape our understanding of the term "functional analysis" itself, as has the celebrated journal Functional Analysis and Its Applications, which he edited for many years. Functional analysis appeared at the beginning of the century in the classic papers of Hilbert on integral operators. Its crucial aspect was the geometric interpretation of families of functions as infinite-dimensional spaces, and of op­ erators (particularly differential and integral operators) as infinite-dimensional analogues of matrices, directlyleading to the geometrization of spectral theory. This view of functional analysis as infinite-dimensional geometry organically included many facets of nineteenth-century classical analysis, such as power series, Fourier series and integrals, and other integral transforms.

• Geometric Quantum Field Theory
• Representation Theory
• calculus
• functional analysis
• geometry
• linear optimization
• operator

• Department of Mathematics, Rutgers University, New Brunswick, USA

  Simon Gindikin, James Lepowsky, Robert L. Wilson

Policies and ethics