Der Grad erzeugender Funktionen von Invariantenringen
(joint work with Peter Littelmann)
Let G be a semisimple group and V a finite-dimensional faithful
representation of G. The ring of invariants is graded which gives rise to a
generating function h(t). This function satisfies a functional equation
h(1/t)=±t^q h(t). In an earlier paper, it was
shown that q<=dim V. Furthermore, equality holds if and only if the set
of all v in V with positive dimensional isotropy group has at least
codimension two. This condition is satisfied for all "generic"
representations.
In the paper, all pairs (G,V) with q<dim V are classified where G
is simple or V is irreducible. Also q is computed for all of these
cases.
Appeared in: Mathematische Zeitschrift 196
(1987) 211--230
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Last updated: August 25, 2006