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Hecke Algebra Questions and Answers

Hecke algebra was studied by who? 
Hecke algebra has which of the following subgroups? 
How can the algebra also be interpreted? An algebra of... 
Which Hecke algebra can be used to prove Macdonald's term conjecture for Macdonald polynomials? 
What is an abstract group that admits a formal description in terms of reflections or kaleidoscopic mirrors? 
A polyhedron whose symmetry group acts transitively on its flags is?
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