2008/11/26 by Kürşat Aker, Aker, Kürşat, Mahir Bilen Can +4
Mathematics · #05E15 #20G40 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05E15 #msc:20G40
paper · pdf · doi:10.48550/arxiv.0811.4382
12 pages
arxiv created 2008/11/26 · openalex publication_date 2008/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citePutcha97 that the Kazhdan-Lusztig involution (\citeKL79) 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.