On tempered and square integrable representations of classical p-adic groups

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.

This paper has two aims.The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data obtained by M glin and the author of this article(2002).The second aim of the paper is to give a description of an invariant(partially defined function)of irreducible square integrable representation of a classical p-adic group(defined by M glin using embeddings)in terms of subquotients of Jacquet modules.As an application,we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group(which is related to deformation of Jordan blocks of representations).