University of Sydney
School of Mathematics and Statistics
University of São Paulo
Representations of Weyl algebras.
Friday October 5, 12-1pm,
A well-known first Weyl algebra A(1) over a field K
is generated by two differential operators on K[x],
multiplication by x and d/dx. Its simple modules
were classified by R.Block in the case of algebraically closed
K of characteristic 0. Later the theory has been
extended to an arbitrary field. The case of the n-th Weyl algebra
A(n)=A(1)×...×A(1) (n times),
n>1, is much more difficult. V.Bavula and F.van Oystaeyen
used a realization of the algebra A(n) as a "generalized Weyl
algebra" in their study of holonomic modules. Following this approach
one can obtain a large class of simple and indecomposable modules for
an arbitrary field K. Recent results in this direction (joint with
V.Bekkert and G.Benkart) will be discussed.
This talk is completely independent of the first talk.