کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4593709 | 1630668 | 2015 | 28 صفحه PDF | دانلود رایگان |
We show that elements of a natural basis of the Iwahori fixed vectors in a principal series representation of a reductive p-adic group satisfy certain recursive relations. The precise identities involve operators that are variants of the Demazure–Lusztig operators, with correction terms, which may be calculated by a combinatorial algorithm that is identical to the computation of the fibers of the Bott–Samelson resolution of a Schubert variety. This leads to an action of the affine Hecke algebra on functions on the maximal torus of the L-group. A closely related action was previously described by Lusztig using equivariant K-theory of the flag variety, leading to the proof of the Deligne–Langlands conjecture by Kazhdan and Lusztig. In the present paper, the action is applied to give a simple formula for the basis vectors of the Iwahori Whittaker functions. We also show that these Whittaker functions can be expressed as non-symmetric Macdonald polynomials.
Journal: Journal of Number Theory - Volume 146, January 2015, Pages 41–68