| 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" |
| 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 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 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/701492 |
| . |
