UBC Mathematics Department
http://www.math.ubc.ca
In his thesis, UBC 1974, P.N. Hoefsmit gave an amazing construction of the irreducible representations of the Iwahori-Hecke algebras of classical type. It was not clear from his work how he arrived at these representations or whether he just guessed and then proved that the guess was correct. I will explain how one can {\it derive} Hoefsmit's representations in an elementary way and without the use of any fancy representation theory. The necessary tools are only some combinatorics and basic linear algebra. Once we have this method of deriving the representations the method can be used to provide analogues of these representations for Iwahori-Hecke algebras of other types.
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