Algebraic Groups and Lie Groups

ISBN-13: 9780521585323 / Angielski / Miękka / 1997 / 396 str.

G. I. Lehrer; Gus Lehrer

Opis

This volume is a unique and comprehensive collection of works by some of the world's leading researchers. Papers on algebraic geometry, algebraic groups, and Lie groups are woven together to form a connection between the study of symmetry and certain algebraic structures. This connection reflects the interests of R. W. Richardson who studied the links between representation theory and the structure and geometry of algebraic groups. In particular, the papers address Kazhdan-Lusztig theory, quantum groups, spherical varieties, symmetric varieties, cohomology of varieties, purity, Schubert geometry, invariant theory and symmetry breaking. For those working on algebraic and Lie groups, this book will be a wealth of fascinating material.

Spis treści

1. Class functions, conjugacy classes and commutators in semisimple Lie theory A. Borel; 2. Curves and divisors in spherical varieties M. Brion; 3. The phylon group and statistics A. Carey, P. Jupp and M. K. Murray; 4. The span of the tangent cones of a Schubert variety J. Carrell; 5. Canonical bases, reduced words and Lusztig's piecewise-linear function R. Carter; 6. Geometric rationality of Satake compactifications W. A. Casselman; 7. Graded and non-graded Kazhdan-Lusztig theories E. Cline, B. Parshall and L. Scott; 8. Quantum Schubert cells and representations at roots of 1 C. de Concini and C. Procesi; 9. Purity and equivariant weight polynomials A. Dimca and G. Lehrer; 10. The restriction of the regular module for a quantum group S. Donkin; 11. On coefficients in Kazhdan-Lusztig polynomials M. Dyer; 12. Spectral estimates for positive Rocklands operators A. F. M. Ter Elst and D. W. Robinson; 13. Factorization of certain exponentials in Lie groups C. K. Fan and G. Lusztig; 14. Symmetry breaking for equivariant maps M. Field; 15. Low dimensional representations of reductive groups J. C. Jantzen; 16. Grosses cellules pour les variétés sphériques D. Luna; 17. Total positivity and canonical bases G. Lusztig; 18. On the number of orbits of a parabolic subgroup on its unipotent radical V. Popov and G. Röhrle; 19. On a homomorphism of Harish-Chandra G. W. Schwarz; 20. Two notes on a finiteness problem in the representation theory of finite groups P. Slodowy; 21. A description of B-orbits on symmetric varieties T. A. Springer; 22. Nagata's example R. Steinberg.