On the structure constants of certain Hecke algebras

Helversen-Pasotto, Anna. "On the structure constants of certain Hecke algebras." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1991. [179]-188. <http://eudml.org/doc/220123>.

@inProceedings{Helversen1991,
abstract = {[For the entire collection see Zbl 0742.00067.]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.Let us mention that meanwhile a parallel proof of the finite a!},
author = {Helversen-Pasotto, Anna},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics},
location = {Palermo},
pages = {[179]-188},
publisher = {Circolo Matematico di Palermo},
title = {On the structure constants of certain Hecke algebras},
url = {http://eudml.org/doc/220123},
year = {1991},
}

TY - CLSWK
AU - Helversen-Pasotto, Anna
TI - On the structure constants of certain Hecke algebras
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1991
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [179]
EP - 188
AB - [For the entire collection see Zbl 0742.00067.]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.Let us mention that meanwhile a parallel proof of the finite a!
KW - Srni (Czechoslovakia); Proceedings; Winter school; Geometry; Physics
UR - http://eudml.org/doc/220123
ER -