R-polynomials of finite monoids of lie type
International Journal of Algebra and Computation, cilt.20, sa.6, ss.793-805, 2010 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 6
- Basım Tarihi: 2010
- Doi Numarası: 10.1142/s0218196710005893
- Dergi Adı: International Journal of Algebra and Computation
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.793-805
- Anahtar Kelimeler: BruhatChevalley ordering, KazhdanLusztig involution, orbit Hecke algebras, R-polynomials, Reductive monoids
- Boğaziçi Üniversitesi Adresli: Evet
Özet
This paper studies the combinatorics of the orbit Hecke algebras associated with W × W orbits in the Renner monoid of a finite monoid of Lie type, M, where W is the Weyl group associated with M. It is shown by Putcha in [12] that the KazhdanLusztig 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 BruhatChevalley 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. © 2010 World Scientific Publishing Company.