# New Developments in Lie Theory and Geometry

Share this page *Edited by *
*Carolyn S. Gordon; Juan Tirao; Jorge A. Vargas; Joseph A. Wolf*

This volume is an outgrowth of the Sixth Workshop on Lie Theory and
Geometry, held in the province of Córdoba, Argentina in
November 2007.

The representation theory and structure theory of Lie groups play a
pervasive role throughout mathematics and physics. Lie groups are
tightly intertwined with geometry and each stimulates developments in
the other. The aim of this volume is to bring to a larger audience
the mutually beneficial interaction between Lie theorists and
geometers that animated the workshop.

Two prominent themes of the representation theoretic articles are
Gelfand pairs and the representation theory of real reductive Lie
groups. Among the more geometric articles are an exposition of major
recent developments on noncompact homogeneous Einstein manifolds and
aspects of inverse spectral geometry presented in settings accessible
to readers new to the area.

# Table of Contents

## New Developments in Lie Theory and Geometry

- Contents v7 free
- Preface vii9 free
- Einstein solvmanifolds and nilsolitons 113 free
- 1. Introduction 113
- 2. Structure and uniqueness results on Einstein solvmanifolds 517
- 3. Technical background 921
- 4. Variational approach to Einstein solvmanifolds 1123
- 5. On the classification of Einstein solvmanifolds 1426
- 6. Known examples and non examples 1931
- 7. A stratification for the variety of nilpotent Lie algebras 2133
- 8. The stratification and the standard condition 2537
- 9. The stratification and Einstein solvmanifolds via closed orbits 2739
- 10. Open problems 2840
- 11. Appendix: Real geometric invariant theory 2941
- References 3244

- Algebraic sets associated to isoparametric submanifolds 3749
- Mostow strong rigidity and nonisomorphism for outer automorphism groups of free groups and mapping class groups 5769
- Spectral properties of flat manifolds 8395
- Heat content, heat trace, and isospectrality 115127
- LR-algebras 125137
- Combinatorial properties of generalized binomial coefficients 141153
- Spherical functions for the action of a finite unitary group on a finite Heisenberg group 151163
- Application of the Weil representation: diagonalization of the discrete Fourier transform 167179
- Infinite dimensional multiplicity free spaces II: Limits of commutative nilmanifolds 179191
- Certain components of Springer fibers: algorithms, examples and applications 209221
- Weighted Vogan diagrams associated to real nilpotent orbits 239251
- The Gelfand-Zeitlin integrable system and its action on generic elements of gl(n) and so(n) 255267
- Closed orbits of semisimple group actions and the real Hilbert-Mumford function 283295
- New techniques for pointed Hopf algebras 323335