Erratum to: On Kazhdan–Lusztig cells in type B

Abstract

In [2], we have found, using brute force computations, some (not all) KazhdanLusztig relations (let us call them the elementary relations) between very particular elements of a Weyl group of type B. This shows in particular that the equivalence classes generated by the elementary relations are contained in Kazhdan-Lusztig cells.It was announced in [6, Theorems 1.2 and 1.3] that the elementary relations generate the equivalence classes defined by the domino insertion algorithm (let us call them the combinatorial cells). As a consequence, we "deduced" that the combinato-

Vogan classes in type $B_n$

“…As y ≈ w and β(w)(n) > 0, it must be the case that β(y)(n) > 0. By Proposition 7.10 (ii), we have: (5) ν(y)(n) > 0 for all ν ∈ V Ξ .…”

“…These conjectures state conditions for two weight functions on W n to be cell-equivalent, as well as a unified combinatorial description of the left, right and two-sided cells for each of these cases. Although there are results in this direction due to Bonnafé [4] [5], a proof of these conjectures remains elusive.…”