Title:

On the structure constants of certain Hecke algebras (English) 
Author:

HelversenPasotto, Anna 
Language:

English 
Journal:

Proceedings of the Winter School "Geometry and Physics" 
Volume:


Issue:

1990 
Year:


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 Mellintransformation. 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 gammafunction 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:

20090713T21:27:29Z 
Last updated:

20120918 
Stable URL:

http://hdl.handle.net/10338.dmlcz/701492 
. 