TY - JOUR
T1 - Iwahori-Hecke algebras for p-adic loop groups
AU - Braverman, Alexander
AU - Kazhdan, David
AU - Patnaik, Manish M.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.
PY - 2016/9/15
Y1 - 2016/9/15
N2 - This paper is a continuation of Braverman and Kazhdan (AnnMath (2) 174(3):1603-1642, 2011) inwhich the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik’s double affine Hecke algebra. Furthermore, using these results,we give an explicit description of the affine Satake isomorphism, generalizing Macdonald’s formula for the spherical function in the finite-dimensional case. The results of this paper have been previously announced in Braverman and Kazhdan (European Congress of Mathematics. European Mathematical Society, Zürich, 2014).
AB - This paper is a continuation of Braverman and Kazhdan (AnnMath (2) 174(3):1603-1642, 2011) inwhich the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik’s double affine Hecke algebra. Furthermore, using these results,we give an explicit description of the affine Satake isomorphism, generalizing Macdonald’s formula for the spherical function in the finite-dimensional case. The results of this paper have been previously announced in Braverman and Kazhdan (European Congress of Mathematics. European Mathematical Society, Zürich, 2014).
UR - http://www.scopus.com/inward/record.url?scp=84941670367&partnerID=8YFLogxK
U2 - 10.1007/s00222-015-0612-x
DO - 10.1007/s00222-015-0612-x
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AN - SCOPUS:84941670367
SN - 0020-9910
VL - 204
SP - 347
EP - 442
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -