**UBC Mathematics Department**

*http://www.math.ubc.ca*

## Colloquium Abstract: Dr. Arun Ram,
Princeton University and MSRI

* Another look at Hoefsmit's representations
*

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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