Representation Theory of Symmetric Spaces over Finite or Local Fields

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As a natural generalization of the representation theory of reductive groups, we studied representations of symmetric spaces attached to these groups. In the case of groups over p-adic fields, we established criteria for (relatively) cuspidal representations and square-integral representations in the form analogous to the group case. Moreover we proved the symmetric space version of subrepresentation theorem. In the case of groups over finite fields, we studied a construction of cuspidal representations on symmetric spaces by cohomological induction.