The University of Michigan Combinatorics Seminar
At least since the work of Iwahori and Tits from the 1960's, and more recent work of Stanley in the 1980's, it has been known that reduced expressions in Coxeter groups have an interesting and non-trivial combinatorial structure. In this talk, we will discuss the particular case of reflections. For example, the number of reduced expressions for a reflection is always expressible as a sum of squares in a canonical way, and in some cases (such as the longest reflection in any Weyl group) there are explicit product formulas for these squares. Also, the reduced expressions for any reflection in a Weyl group can be viewed as the linear extensions of a naturally associated poset, even though the corresponding portion of the weak order is not a distributive lattice.