Abstract
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, 17, 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 2 × 2 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 × n matrices for n > 2.
This work is partially supported by an NSF Grant.
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References
I. Bernstein, P-invariant distributions on GL(N), Lecture Notes in Math. 1041(1984), Springer-Verlag, 50–102.
I. Bernstein, A. Zelevinsky, Induced representations of reductive p-adic groups, I. Ann. Scien. Ec. Norm. Sup., 4e série, t. 10(1977), 441–472.
I. Gelfand, D. Kazhdan, Representations of GL(n, K)in Lie Groups and their Representations, John Wiley and Sons, 1975, 95–118.
I. Gelfand, M. Graev, I. Piatetsky-Shapiro, Representation theory and automorphic functions, Saunders: London, 1969.
H. Jacquet, I. Piatetsky-Shapiro, J. Shalika, Automorphic forms on GL(3), I. Ann. of Math., 109: 1 (1979), 169–212.
D. Kazhdan, The minimal representation of D 4 in Operator algebras, Unitary representations, Enveloping Algebras and Invariant Theory, Progress in Mathematics 92 1990, Birkhäuser, 127–158.
D. Kazhdan and G. Laumon, Gluing of perverse sheaves and discrete series representations, J. Geometry and Physics, 5:1 (1988), 63–120.
A. Weil, Adèles et groupes algébriques, Séminaire Bourbaki, mai 1959, n° 186.
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Kazhdan, D. (1995). “Forms” of the Principal Series for GL n . In: Gindikin, S., Lepowsky, J., Wilson, R.L. (eds) Functional Analysis on the Eve of the 21st Century. Progress in Mathematics, vol 131/132. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2582-9_5
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DOI: https://doi.org/10.1007/978-1-4612-2582-9_5
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