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

2022/07/06 by Luo, Caihua
#11F66 #11F70 #17B22 #22E35 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2207.02694

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.

Related

• Casselman-Shahidi's conjecture on normalized intertwining operators for groups of classical type
• Holomorphy of normalized intertwining operators for certain induced representations I: a toy example
• Local Intertwining Relations and Co-tempered A-packets of Classical Groups
• The bijection between exceptional subcategories and non-crossing partitions
• Separable elements and splittings in Weyl groups of Type B