
School of Mathematics and Statistics
Alex Molev
University of Sydney
Extremal projections for reductive Lie algebras.
Friday 8th October, 121pm, Carslaw 375.
Given a module V over a complex reductive Lie algebra a,
the extremal projection p=p(a) takes V into the
subspace of its extreme (highest) vectors.
The projection p can be given by a universal explicit
formula independent of the module V.
A theorem of Zhelobenko states that p
is a unique element of an extension of
the enveloping algebra U(a) satisfying
certain natural conditions.
The method of extremal projections
and its applications will be discussed in the talk.
In particular, a simple construction of
a basis in the harmonic polynomials will be given
with the use of the projection p=p(sl(2)).
