Whittaker Modules for Generalized Weyl Algebras

Details Whittaker Modules for Generalized Weyl Algebras Whittaker Modules for Generalized Weyl Algebras

2008-03-25

arxiv.org/abs/0803.3570v1

Mathematics

Representation Theory

34 pages

Scientific paper

We investigate Whittaker modules for generalized Weyl algebras, a class of associative algebras which includes the quantum plane, Weyl algebras, the universal enveloping algebra of sl_2 and of Heisenberg Lie algebras, Smith's generalizations of U(sl_2), various quantum analogues of these algebras, and many others. We show that the Whittaker modules V = Aw of the generalized Weyl algebra A = R(phi,t) are in bijection with the phi-stable left ideals of R. We determine the annihilator Ann_A(w) of the cyclic generator w of V. We also describe the annihilator ideal Ann_A(V) under certain assumptions that hold for most of the examples mentioned above. As one special case, we recover Kostant's well-known results on Whittaker modules and their associated annihilators for U(sl_2).

Affiliated with

Also associated with

No associations

Rating

Whittaker Modules for Generalized Weyl Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Whittaker Modules for Generalized Weyl Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Whittaker Modules for Generalized Weyl Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-349294