On Multiplicity Formula for Spherical Varieties

Abstract

In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker model, Gan-Gross-Prasad model, Ginzburg-Rallis model, Galois model and Shalika model, we show that the multiplicity formula in our conjecture matches the multiplicity formula that has been proved. We also give a proof of this multiplicity formula in two new cases.

Add the proof of the multiplicity formula of K-types for GL(n) and for all the complex reductive groups

References in corpus (2)

• A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case
• The dual group of a spherical variety

Cited by in corpus (3)

• Annihilator varieties of distinguished modules of reductive Lie algebras
• Families of Canonical Local Periods on Spherical Varieties
• Periods of Automorphic Forms Associated to Strongly Tempered Spherical Varieties