The Hecke algebra of a Coxeter group 
is the algebra generated by elements
for the simple reflections, subject
to the braid relations and quadratic relations 
. It is a deformation of the group
algebra of 
and specializes to it when 
.
Hecke Algebra
See also
Coxeter Group, Full p-adic Hecke Algebra, Group Algebra, Hecke Operator, Kazhdan-Lusztig PolynomialExplore with Wolfram|Alpha
References
Geck, M. and Pfeiffer, G. Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras. Oxford, England: Clarendon Press, 2000.Cite this as:
Weisstein, Eric W. "Hecke Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HeckeAlgebra.html