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Search: MSC category 05E15 ( Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] )

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1. CMB 2010 (vol 53 pp. 757)

Woo, Alexander
Interval Pattern Avoidance for Arbitrary Root Systems
We extend the idea of interval pattern avoidance defined by Yong and the author for $S_n$ to arbitrary Weyl groups using the definition of pattern avoidance due to Billey and Braden, and Billey and Postnikov. We show that, as previously shown by Yong and the author for $\operatorname{GL}_n$, interval pattern avoidance is a universal tool for characterizing which Schubert varieties have certain local properties, and where these local properties hold.

Categories:14M15, 05E15

2. CMB 2007 (vol 50 pp. 535)

Hohlweg, Christophe
Generalized Descent Algebras
If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-$\ZM$-module $\DC_A(W)$ of the group algebra $\ZM W$. We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if $W$ is of type $B$, the Mantaci--Reutenauer algebra.

Keywords:Coxeter group, Solomon descent algebra, descent set
Categories:20F55, 05E15

3. CMB 2002 (vol 45 pp. 537)


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