Spherical functions of symmetric forms and a conjecture of Hironaka

2023/10/31 by Corato-Zanarella, Murilo
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2311.00147

Abstract

For all r≥1, we verify the following conjecture of Hironaka: for a p-adic field F with p odd, the space of spherical functions of Sym_{r× r}(F)\capGL_r(F) is free of rank 4^r over the Hecke algebra.

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