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

Michael Kapovich; Bernhard Leeb; John J. Millson

ISBN 10: 0821840541 / ISBN 13: 9780821840542

Verlag: Amer Mathematical Society, 2008

Former library book; Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Bestandsnummer des Verkäufers G0821840541I3N10

Inhaltsangabe:

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 $\mathbb{Q}$.

Bibliografische Details

Titel: The Generalized Triangle Inequalities in ...
Verlag: Amer Mathematical Society
Erscheinungsdatum: 2008
Einband: Paperback
Zustand: Good
Zustand des Schutzumschlags: No Jacket