Geometric structure for the principal series of a split reductive \(p\)-adic group with connected centre (Q740104)

Let \(\mathcal{G}\) be a split reductive \(p\)-adic group with connected centre. The authors show that each Bernstein block in the principal series of \(\mathcal{G}\) admits a geometric structure of an extended quotient. For the Iwahori-spherical block, this extended quotient has the form \(T//W\) where \(T\) is a maximal torus in the Langlands dual group of \(\mathcal{G}\) and \(W\) is the Weyl group of \(\mathcal{G}\).