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Title: On the structure constants of certain Hecke algebras (English)
Author: Helversen-Pasotto, Anna
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1990
Pages: [179]-188
Category: math
Summary: [For the entire collection see Zbl 0742.00067.]\par In the first part some general results on Hecke algebras are recalled; the structure constants corresponding to the standard basis are defined; in the following the example of the commuting algebra of the Gelfand- Graev representation of the general linear group $GL(2,F)$ is examined; here $F$ is a finite field of $q$ elements; the structure constants are explicitly determined first for the standard basis and then for a new basis obtained via a Mellin-transformation. Using the character table of the group $GL(2,F)$ two identities envolving Gaussian sums over finite fields are obtained. One of them is a formal analogue of the classical Barnes' First Lemma; this lemma involves the classical gamma-function which is in analogy with the Gaussian sum function. Three more finite identities are given and several open questions are brought into discussion.\par Let us mention that meanwhile a parallel proof of the finite a! (English)
MSC: 11T24
MSC: 20C15
MSC: 20C33
MSC: 20G05
MSC: 20G40
MSC: 33C80
idZBL: Zbl 0756.20003
idMR: MR1151904
Date available: 2009-07-13T21:27:29Z
Last updated: 2012-09-18
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