33 research outputs found
Shadows in Coxeter groups
For a given in a Coxeter group the elements smaller than in
Bruhat order can be seen as the end-alcoves of stammering galleries of type
in the Coxeter complex . We generalize this notion and consider sets of
end-alcoves of galleries that are positively folded with respect to certain
orientation of . We call these sets shadows. Positively folded
galleries are closely related to the geometric study of affine Deligne-Lusztig
varieties, MV polytopes, Hall-Littlewood polynomials and many more agebraic
structures. In this paper we will introduce various notions of orientations and
hence shadows and study some of their algorithmic properties.Comment: 30 pages, 8 figures, revised and final versio