2018/10/16 by Broussous, Paul
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1810.06910
Let G/H be a reductive symmetric space over a p-adic field F, the algebraic groups G and H being assumed semisimple of relative rank 1. One of the branching problems for the Steinberg representation \StG of G is the determination of the dimension of the intertwining space \rm HomH (\StG ,π), for any irreducible representation π of H. In this work we do not compute this dimension, but show how it is related to the dimensions of some other intertwining spaces \rm HomKi ( π ,1), for a certain finite family Ki, i=1,...,r, of anisotropic subgroups of H (here π denote the contragredient representation, and 1 the trivial character). In other words we show that there is a sort of `reciprocity law' relating two different branching problems.