On the Maximally Clustered Elements of Coxeter Groups

Deodhar Elements in Kazhdan-Lusztig Theory

The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all positive interpretation for them is known in general. Deodhar has given a framework, which generally involves recursion, to express the Kazhdan-Lusz...

CLASSIFICATION OF COXETER GROUPS WITH FINITELY MANY ELEMENTS OF a-VALUE 2

We consider Lusztig’s a-function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of a-value 2 in terms of Coxeter diagrams.

Essays on Coxeter groups Coxeter elements in finite Coxeter groups

A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...

Complete Growth Series of Coxeter Groups with more than Three Generators

Characterization of cyclically fully commutative elements in finite and affine Coxeter groups

An element of a Coxeter group is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. An element of a Coxeter group is cyclically fully commutative if any of its cyclic shifts remains fully commutative. These elements were studied by Boothby et al. In particular the authors precisely identified the Coxeter groups ...