On the combinatorics of B × B-orbits on group compactifications

2002/10/20 by Yu Chen, Chen, Yu, Matthew Dyer +1
Mathematics · #22E47 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:22E47

paper · pdf · doi:10.48550/arxiv.math/0210311

14 pages

arxiv created 2002/10/20 · arxiv updated 2009/11/30

Abstract

It is shown that there is an order isomorphism ϕ' from the poset V of B× B-orbits on the wonderful compactification of a semi-simple adjoint group G with Weyl group W to an interval in reverse Chevalley-Bruhat order on a non-canonically associated Coxeter group W (in general neither finite nor affine). Moreover, ϕ' preserves the corresponding Kazhdan-Lusztig polynomials. Springer's (partly conjectural) construction of Kazhdan-Lusztig polynomials for the analogues of V for general Coxeter groups W is completed by reducing it by a similar order isomorphism to known results involving a ``twisted'' Chevalley-Bruhat order on W.

Related

• The intermediate orders of a Coxeter group
• Classifying quotients on Coxeter groups by isomorphism in Bruhat order
• Fixed points of involutive automorphisms of the Bruhat order
• Twisted identities in Coxeter groups
• Note sur les polynomes de Kazhdan-Lusztig