Finite Hecke algebras
Last update: 23 December 2012
Let be an indeterminate and let
The Hecke algebra is presented by generators
, and relations
The conversion between the two presentations is given by the relations
be an indeterminate and let
HOW SHOULD WE DEAL WITH THE ISSUE OF MULTIPLE PARAMETERS--PERHAPS AN EXERCISE??
The finite Hecke algebra
is the algebra over given by generators
is the angle between
The algebra has -basis
Convolution algebra presentation
Let be a finite field with
The Weyl group of is
(a) Let .
(c) The characteristic functions
of the double cosets
are a basis of the Hecke algebra
For the moment, we refer to affflags1.14.07.pdf for the proof.
Notes and References
These notes are intended to supplement various lecture series given by Arun Ram.
These important facts about Iwahori-Hecke algebras are found in Bourbaki ????.
The original papers are [Iw] Iwahori ????, and [IM] Iwahori-Matsumoto ????.
One can also see Steinberg Lecture notes ?????.