The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra

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

ISBN 10: 0821840541 / ISBN 13: 9780821840542

Published by American Mathematical Society, Providence, RI, 2008

About this Item

Memoirs of the American Mathematical Society, number 896. Slender softback, in very good condition, from the collection of a London Professor of Mathematics, (ret'd.). Light shelf and handling wear, including minor creasing to corners. Within, pages tightly bound, content unmarked. CN.

Seller Inventory # 616320

Bibliographic Details

• Title: The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra
• Publisher: American Mathematical Society, Providence, RI
• Publication Date: 2008
• Language: English
• ISBN 10: 0821840541
• ISBN 13: 9780821840542
• Binding: Paperback
• Condition: Very Good
• Seller catalogs:
  • Mathematics/Accounting

About this title

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 $\mathbb{Q}$.