The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra (Memoirs of the American Mathematical Society) - Softcover

Kapovich, Michael; Leeb, Bernhard; Millson, John J.

Softcover

ISBN 10: 0821840541 ISBN 13: 9780821840542

Publisher: American Mathematical Society, 2008

Synopsis

In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the ""Saturation Conjecture"" for $GL(\ell)$ as a consequence of their solution of the corresponding ""saturation problem"" for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2008
• Language: English
• ISBN 10: 0821840541
• ISBN 13: 9780821840542
• Binding: Paperback
• Number of pages: 83