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On a multiplicity formula for spherical varieties. (English) Zbl 1508.22012

Summary: 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 models, Gan-Gross-Prasad models, Ginzburg-Rallis models, Galois models and Shalika models, we show that the multiplicity formulas in our conjecture are the same as the multiplicity formulas that have been proved. We also prove the conjectural multiplicity formula in two new cases.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
14M27 Compactifications; symmetric and spherical varieties
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