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arXiv · 2207.02694

Casselman--Shahidi conjecture on the singularity of intertwining operators: groups of exceptional type

Caihua Luo
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Abstract

As a sequel to our recent work on Casselman--Shahidi's holomorphicity conjecture on half-normalized intertwining operators for quasi-split classical groups, we modify our method, based on a lemma of Heiermann--Opdam, to prove certain cases of the conjecture for groups of exceptional type uniformly. One main ingredient, established here, is to find an algorithm to produce reduced decompositions of co-rank one relative longest Weyl elements, in terms of certain "small" counterparts.

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Caihua Luo. 2022-07-06. Casselman--Shahidi conjecture on the singularity of intertwining operators: groups of exceptional type. https://arxiv.org/abs/2207.02694

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