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Geometric structure for the principal series of a split reductive \(p\)-adic group with connected centre. (English) Zbl 1347.22013
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 \(\mathcal{G}\).
Reviewer: Hu Jun (Beijing)

22E50 Representations of Lie and linear algebraic groups over local fields
20G05 Representation theory for linear algebraic groups
Full Text: DOI arXiv
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