(Ben Gurion University)
"Multiplicities of Cuspidal Representations"
Abstract: For any abstract representation p of an adelic group G it is an important problem to compute multiplicity m(p) at which it occurs in the cuspidal spectrum. It was known for a long time that if G=GL_n then m(p)<= 1 for any p. Recently it was also proved for G=SL_2. This is no longer true when G is an inner form of SL_2 or G=SL_n, n >= 3. We will explain these results and expectations for other groups using a conjectured Arthur's multiplicity formula.