Fixed points of involutive automorphisms of the Bruhat order
By Axel Hultman. 2004
51 citations recorded by the source corpus.
Abstract Applying a classical theorem of Smith, we show that the poset property of being Gorenstein * over Z 2 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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d44776e542f9d4539cbe790052a32cd2475d9498
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The combinatorics of twisted involutions in Coxeter groups (2004, background): “8] that Br(I(θ)) is graded with rank function ρ and that ρ(w) = ( (w) + (w))/2 for all w ∈ I(θ), where θ is the twisted absolute length function (see [16] for the definition).”