Induced representations and intertwining operators give rise to distributions that represent critical terms in the trace formula. We shall describe a conjectural relationship between these distributions and the LanglandsShelstad-Kottwitz transfer of functions Our goal is to describe a conjectural relationship between intertwining operators and the transfer of functions. One side of the proposed...

1. Residues . ..... ........ .... ... .... 54 2. ir-discrete distributions ............... . .. . . .. . 58 3. Admissible families of operators .......... ............. 67 4. The main formula ............. ... ............ 74 5. Completion of the induction argument .................... 83 6. Cuspidal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7. Conclusions ..............

For each of the two series of groups, three series of representations U„, D„, and H„ (n e Z) are considered. For each series of representations there is a differential operator with the property, that raised to the nth power (n > 0), it intertwines the representations indexed by — n and n. The operators are generalizations of the d'Alembertian, the Diracoperator and a combination of the two. Un...

In this paper we discuss a general strategy to construct vector coherent states of the Gazeau-Klauder type and we use them to built up examples of isospectral hamiltonians. For that we use a general strategy recently proposed by the author and which extends well known facts on intertwining operators. We also discuss the possibility of constructing non-isospectral hamiltonians with related eigen...