Symmetry: Representation Theory and Its Applications

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.

Preface. - Publications of Nolan R. Wallach. - Unitary Hecke algebra modules with nonzero Dirac cohomology. - On the nilradical of a parabolic subgroup. - Arithmetic invariant theory. - Structure constants of Kac-Moody Lie algebras. - The Gelfand-Zeitlin integrable system and K-orbits on the flag variety. - Diagrams of Hermitian type, highest weight modules, and syzygies of determinantal varieties. - A conjecture of Sakellaridis-Venkatesh on the unitary spectrum of spherical varieties. - Proof of the 2-part compositional shuffle conjecture. - On symmetric SL-invariant polynomials in four qubits. - Finite maximal tori. - Sums of Littlewood Richardson coefficients and GLn-harmonic polynomials. - Polynomial functors and categorifications of Fock space. - Pieri algebras and Hibi algebras in representation theory. - Action of the conformal group on steady state solutions to Maxwell s equations and background radiation. - Representations with a reduced null cone. - M-series and Kloosterman Selberg zetafunctions for R-rank one groups. - Ricci flow and manifolds with positive curvature. - Remainder formula and zeta expression for extremal CFT partition functions. - Principal series representations of infinite-dimensional Lie groups, I: Minimal parabolic subgroups.