$R$-polynomials of finite monoids of Lie type

Aker, Kürşat; Can, Mahir Bilen; Taşkín, Müge

$R$-polynomials of finite monoids of Lie type

Authors

Aker, Kürşat

Can, Mahir Bilen

Taşkín, Müge

Description

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 \cite{Putcha97} that the Kazhdan-Lusztig involution (\cite{KL79}) 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.
12 pages