Ext-distinction for p-adic symmetric spaces

2023/12/18 by Yang, Chang
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2312.10974

Abstract

Let G/H be a p-adic symmetric space. We compute explicitly the higher relative extension groups for all discrete series representations of G in two examples: the symplectic case and the linear case. The results have immediate applications to the computation of the Euler-Poincaré pairing, the alternating sum of the dimensions of the Ext-groups. In the linear case we confirm a conjecture of Wan which asserts the equality of the Euler-Poincaré pairing with the geometric multiplicity for any irreducible representation of G. In the symplectic case we reduce the verification of Wan's conjecture to the case of discrete series representations. We also determine all relatively supercuspidal representations in both cases.

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