New Developments in Lie Theory and Geometry.

Intro -- Contents -- Preface -- Einstein solvmanifolds and nilsolitons -- 1. Introduction -- 2. Structure and uniqueness results on Einstein solvmanifolds -- 3. Technical background -- 4. Variational approach to Einstein solvmanifolds -- 5. On the classification of Einstein solvmanifolds -- 6. Known examples and non examples -- 7. A stratification for the variety of nilpotent Lie algebras -- 8. The stratification and the standard condition -- 9. The stratification and Einstein solvmanifolds via closed orbits -- 10. Open problems -- 11. Appendix: Real geometric invariant theory -- References -- Algebraic sets associated to isoparametric submanifolds -- Mostow strong rigidity and nonisomorphism for outer automorphism groups of free groups and mapping class groups -- 1. Introduction and statements of results -- 2. Nonisomorphisms between different types of groups -- 3. Proof of Mostow rigidity for Out(Fn) -- 4. Proof of Mostow rigidity for Mod+g,p -- References -- Spectral properties of flat manifolds -- 1. Introduction -- 2. Flat manifolds -- 3. Spectrum and isospectrality of compact flat manifolds -- 4. Closed geodesics -- 5. P-isospectral examples -- 6. Self-intersection of closed geodesics -- 7. Poisson summation formulas -- 8. Flat orbifolds -- References -- Heat content, heat trace, and isospectrality -- LR-algebras -- Combinatorial properties of generalized binomial coefficients -- Spherical functions for the action of a finite unitary group on a finite Heisenberg group -- Application of the Weil representation: diagonalization of the discrete Fourier transform -- Infinite dimensional multiplicity free spaces II: Limits of commutative nilmanifolds -- Certain components of Springer fibers: algorithms, examples and applications -- Weighted Vogan diagrams associated to real nilpotent orbits.

The Gelfand-Zeitlin integrable system and its action on generic elements of gl(n) and so(n) -- Closed orbits of semisimple group actions and the real Hilbert-Mumford function -- Introduction -- Section 1: Moment map and minimal vectors -- Section 2: The set of vectors with closed G-orbits -- Section 3: The M-function -- Section 4: The index method -- Section 5: Examples -- References -- New techniques for pointed Hopf algebras.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.