Vortrag im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 19. Oktober 2007, um 15:00 Uhr in F420 (Oberseminar) Bertfried Fauser (Konstanz)
Einführung in die kombinatorische Darstellungstheorie algebraischer Gruppen unter Verwendung von symmetrischen Funktionen und Hopf-Algebren.
ABSTRACT: Symmetric functions and Young tableaux have been employed in the
representation theory of finite and classical groups since the emergence of the
theory in the 19th century. It was known since the 70ies that Hopf algebra
methods can be employed in this theory. We focus on the branching of group
characters into subgroup characters among those classical cases as for example
the Pieri rule. Recent studies using the Hopf algebra structure opened a new
and explicit approach to the branching problem thereby widening the scope to
algebraic groups having only indecomposable representations. I will introduce
the theory of group branchings and its combinatorially explicite structure and
will review the Hopf algebraic machinery behind. As an application I show how
knot and link invariants can be derived directly< from the branching problem
