Symmetry: Representation Theory and Its Applications

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 Touzé, 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

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.

• Symmetry, Representation Theory, Harmonic Analysis
• combinatorics

• 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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