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Symmetry: Representation Theory and Its Applications

In Honor of Nolan R. Wallach

  • Book
  • © 2014

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Editors:
  1. Roger Howe

    1. Dept. Mathematics 442 Dunham Lab, Yale University, New Haven, USA

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  2. Markus Hunziker

    1. Department of Mathematics, Baylor University, Waco, USA

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  3. Jeb F. Willenbring

    1. Department of Mathematical Sciences EMS Building, Room E403, University of Wisconsin, Milwaukee, Milwaukee, USA

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  • A unique and comprehensive tribute for Nolan R. Wallach, a mathematician with far-reaching expertise in a number of fields
  • Includes expository articles that will be accessible to a broad audience
  • Serves as an excellent reference tool for graduate students, mathematicians, and physicists interested in representation theory and its applications
  • Contributions from top-rate mathematicians

Part of the book series: Progress in Mathematics (PM, volume 257)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xxviii
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  2. Unitary Hecke algebra modules with nonzero Dirac cohomology

    • Dan Barbasch, Dan Ciubotaru
    Pages 1-20

  3. On the nilradical of a parabolic subgroup

    • Karin Baur
    Pages 21-32

  4. Arithmetic invariant theory

    • Manjul Bhargava, Benedict H. Gross
    Pages 33-54

  5. Structure constants of Kac–Moody Lie algebras

    • Bill Casselman
    Pages 55-83

  6. The Gelfand–Zeitlin integrable system and K-orbits on the flag variety

    • Mark Colarusso, Sam Evens
    Pages 85-119

  7. Diagrams of Hermitian type, highest weight modules, and syzygies of determinantal varieties

    • Thomas J. Enright, Markus Hunziker, W. Andrew Pruett
    Pages 121-184

  8. A conjecture of Sakellaridis–Venkatesh on the unitary spectrum of spherical varieties

    • Wee Teck Gan, Raul Gomez
    Pages 185-226

  9. Proof of the 2-part compositional shuffle conjecture

    • Adriano M. Garsia, Gouce Xin, Mike Zabrocki
    Pages 227-257

  10. On symmetric SL-invariant polynomials in four qubits

    • Gilad Gour, Nolan R. Wallach
    Pages 259-267

  11. Finite maximal tori

    • Gang Han, David A. Vogan Jr.
    Pages 269-303

  12. Sums of squares of Littlewood–Richardson coefficients and GL n -harmonic polynomials

    • Pamela E. Harris, Jeb F. Willenbring
    Pages 305-326

  13. Polynomial functors and categorifications of Fock space

    • Jiuzu Hong, Antoine TouzĂ©, Oded Yacobi
    Pages 327-352

  14. Pieri algebras and Hibi algebras in representation theory

    • Roger Howe
    Pages 353-384

  15. Action of the conformal group on steady state solutions to Maxwell’s equations and background radiation

    • Bertram Kostant, Nolan R. Wallach
    Pages 385-418

  16. Representations with a reduced null cone

    • Hanspeter Kraft, Gerald W. Schwarz
    Pages 419-474

  17. M-series and Kloosterman–Selberg zeta functions for ℝ-rank one groups

    • Roberto J. Miatello, Nolan R. Wallach
    Pages 475-490

  18. Ricci flow and manifolds with positive curvature

    • Lei Ni
    Pages 491-504

  19. Remainder formula and zeta expression for extremal CFT partition functions

    • Floyd L. Williams
    Pages 505-518

  20. Principal series representations of infinite-dimensional Lie groups, I: Minimal parabolic subgroups

    • Joseph A. Wolf
    Pages 519-538
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Keywords

About this book

Nolan Wallach's mathematical research is remarkable in both its breadth and  depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.

Editors and Affiliations

  • Dept. Mathematics 442 Dunham Lab, Yale University, New Haven, USA

    Roger Howe

  • Department of Mathematics, Baylor University, Waco, USA

    Markus Hunziker

  • Department of Mathematical Sciences EMS Building, Room E403, University of Wisconsin, Milwaukee, Milwaukee, USA

    Jeb F. Willenbring

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