Hubert Rubenthaler
Invariant differential operators on a class of multiplicity free spaces.
Thu, 03/10/2011 - 16:01 — SomNambulAuthors: Hubert Rubenthaler
Subjects: Representation Theory
AbstractIf $Q$ is a non degenerate quadratic form on ${\bb C}^n$, it is well known
that the differential operators $X=Q(x)$, $Y=Q(\partial)$, and
$H=E+\frac{n}{2}$, where $E$ is the Euler operator, generate a Lie algebra
isomorphic to ${\go sl}_{2}$.Algebras of invariant differential operators on a class of multiplicity free spaces.
Fri, 10/30/2009 - 16:01 — SomNambulAuthors: Hubert Rubenthaler
Subjects: Representation Theory
AbstractLet G be a connected reductive algebraic group and let G'=[G,G] be its
derived subgroup. Let (G,V) be a multiplicity free representation with a one
dimensional quotient (see definition below). We prove that the algebra
D(V)^{G'} of G'-invariant differential operators with polynomial coefficients
on V, is a quotient of a so-called Smith algebra over its center. Over C this
class of algebras was introduced by S.P. Smith as a class of algebras similar
to the enveloping algebra U(sl(2)) of sl(2).
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