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arXiv · 0811.4382

$R$-polynomials of finite monoids of Lie type

Kürşat Aker·Mahir Bilen Can·Müge Taşkín
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Abstract

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.

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Kürşat Aker, Mahir Bilen Can, Müge Taşkín. 2008-11-26. $R$-polynomials of finite monoids of Lie type. https://arxiv.org/abs/0811.4382

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