Quasi-minuscule quotients and reduced words for reflections (Q5939549)

The author studies the reduced expressions for reflections in Coxeter groups. He obtains an explicit formula for the number of reduced expressions for the longest reflection in any finite Weyl group. He also shows that in a finite Weyl group, the Cayley order associated with any reflection can be deformed into a distributive lattice in a way that preserves the number of maximal chains. Thus the reduced expressions for a reflection are in one-to-one correspondence with the linear extensions of some poset.