2004/03/04 by Axel Hultman, Hultman, Axel
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.math/0403095
16 pages. Appendix added, minor revisions; to appear in Adv. Math
arxiv created 2004/10/14 · arxiv updated 2009/12/01
Applying a classical theorem of Smith, we show that the poset property of being Gorenstein^* over ℤ2 is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. Incitti. We also show that the Bruhat order on the fixed points of an involutive automorphism induced by a Coxeter graph automorphism is isomorphic to the Bruhat order on the fixed subgroup viewed as a Coxeter group in its own right.