“Forms” of the Principal Series for GLn
I am very grateful to the organizers of the conference in honor of I.M. Gelfand’s 80th birthday. Professor Gelfand has built a remarkable school of mathematics and I am proud to belong to this school. I have learned the theory of group representations from the works of I.M. Gelfand and his collaborators. One of the papers which made the strongest impression was the paper of Gelfand and Graev Representations of the real unimodular group (Isvestia Academy of USSR, IT, 1953, 189–248) which teaches us that the series of representations of real semisimple groups can be obtained from the principal series by a kind of “analytic continuation”. This point of view was extended to the group of p-adic 2x2 matrices in the book [G-G-PS] of Gelfand, Graev and Piatetsky-Shapiro. This paper is an attempt to construct the notion of “forms” of representations for the group of p-adic n x n matrices for n > 2.
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