Iwahori-Hecke algebra of the symmetric group
Let be a unital ring and be a natural number. The Iwahori-Hecke algebra of the symmetric group of degree over the ring is defined as the -algebra given by the presentation:
In other words, it is the Iwahori-Hecke algebra corresponding to the symmetric group of degree , viewed as a Coxeter group, in the usual way: Symmetric group on a finite set is a Coxeter group.
For a field with elements, specializing to the value gives the Hecke algebra of the general linear group .
|Iwahori-Hecke algebra of the symmetric group of degree|
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