R-Polynomials of Finite Monoids of Lie Type

This paper concerns the combinatorics of the orbit Hecke algebra associated with the orbit of a two sided Weyl group action on the Renner monoid of a finite monoid of Lie type, M . It is shown by Putcha in [12] that the Kazhdan-Lusztig involution ([6]) can be extended to the orbit Hecke algebra which enables one to define the R-polynomials of the intervals contained in a given orbit. Using the R-polynomials, we calculate the Möbius function of the Bruhat-Chevalley ordering on the orbits. Furthermore, we provide a necessary condition for an interval contained in a given orbit to be isomorphic to an interval in some Weyl group.