On the Schwartz space of the basic affine space

Details On the Schwartz space of the basic affine space On the Schwartz space of the basic affine space

1998-09-20

arxiv.org/abs/math/9809112v2

Mathematics

Algebraic Geometry

28 pages, LaTeX, no figures; a small mistake in Section 6 is corrected

Scientific paper

Let G be the group of points of a split reductive algebraic group over a local field k and let X=G/U where U is a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz space of X) of functions on X, which is an extension of the space of smooth compactly supported functions on X. We show that the space of all elements of S(X) invariant under the Iwahori subgroup of G coincides with space generated by the elements of the so called periodic Lusztig's basis, introduced recently by G.Lusztig. We also give an interpretation of this space in terms of certain equivariant K-group (this was also done by G.Lusztig). Finally we present a global analogue of S(X) which allows us to give a somewhat untraditional treatment of the theory of principal Eisenstein series.

Affiliated with

Also associated with

No associations

Rating

On the Schwartz space of the basic affine space 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 On the Schwartz space of the basic affine space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Schwartz space of the basic affine space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-130230