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arXiv · 2508.13817

Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A

Johannes Droschl
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Abstract

In this paper, we propose a conjectural formula for the order of the poles of intertwining operators in the context of the representation theory of general linear groups over $p$-adic fields. More specifically, we conjecturally relate the order of the pole to the dimension of a Hom-space associated with irreducible components of Lusztig's characteristic variety in type $A$. We verify the conjecture in a wide range of cases.

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BibTeXRIS

Johannes Droschl. 2025-08-19. Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A. https://arxiv.org/abs/2508.13817

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