We extend the Shi bijection from the Borel subalgebra case to parabolic
subalgebras. In the process, the I-deleted Shi arrangement Shi(I)
naturally emerges. This arrangement interpolates between the Coxeter
arrangement Cox and the Shi arrangement Shi, and breaks
the symmetry of Shi in a certain symmetrical way. Among other
things, we determine the characteristic polynomial Ο(Shi(I),t)
of Shi(I) explicitly for Anβ1β and Cnβ. More generally, let
Shi(G) be an arbitrary arrangement between Cox and
Shi. Armstrong and Rhoades recently gave a formula for
Ο(Shi(G),t) for Anβ1β. Inspired by their result, we obtain
formulae for Ο(Shi(G),t) for Bnβ, Cnβ and Dnβ.Comment: The third version, quasi-antichains are shown to be in bijection with
elements of L(Cox). arXiv admin note: text overlap with arXiv:1009.1655 by
other author