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Grothendieck topology and the theory of representations. (English. Russian original) Zbl 0239.22006
Funct. Anal. Appl. 5, 188-196 (1972); translation from Funkts. Anal. Prilozh. 5, No. 3, 22-31 (1971).
MSC:
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
22A25 Representations of general topological groups and semigroups
46N99 Miscellaneous applications of functional analysis
18F10 Grothendieck topologies and Grothendieck topoi
20C99 Representation theory of groups
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References:
[1] M. Artin, Grothendieck Topologies, Preprint, Harvard (1962).
[2] I. M. Gel’fand and D. B. Fuks, ”Topology of non-compact Lie groups,” Funktsional. Analiz i ego Prilozhen.,1, No. 4, 33–45 (1967). · Zbl 0161.11601 · doi:10.1007/BF01075864
[3] A. Yu. Geronimus, ”Cohomologies of groups in categories,” Funktsional. Analiz i Ego Prilozhen.,2, No. 3, 86 (1968). · Zbl 0197.19701
[4] A. Yu. Geronimus, ”Lie groups and Grothendieck topology,” Uspekhi Mat. Nauk,26, No. 1, 219–220 (1971). · Zbl 0208.51305
[5] A. Borel, ”Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groupes de Lie compact,” Ann. of Math.,57, 115–207 (1953). · Zbl 0052.40001 · doi:10.2307/1969728
[6] I. M. Gel’fand, M. I. Graev, and N. Ya. Vilenkin, Generalized Functions., Vol. 5. Integral Geometry and Representation Theory [in Russian], Fizmatgiz, Moscow (1962).
[7] I. M. Gel’fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Generalized Functions. Vol. 6. Representation Theory and Automorphic Functions [in Russian], Fizmatgiz, Moscow (1966). · Zbl 0138.07201
[8] A. A. Kirillov, ”Construction of irreducible unitary representations of Lie groups,” Vestnik Moskov. Gos. Univ., Ser. 1, No. 2, 41–50 (1970).
[9] R. Godement, Topologie algebrique et théorie des faiscaux, Hermann, Paris (1958).
[10] J.-P. Serre, Lie Algebras and Lie Groups [Russian translation], Izd. Mir, Moscow (1969).
[11] R. Godement, ”Theory of spherical functions,” [Russian translation], Matematika,5: 5, 55–87 (1961).
[12] D. Mumford, Picard Groups of Moduli Problems. Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963), Harper and Row, New York, pp. 33–81.
[13] Yu. I. Manin, ”The algebraic topology of algebraic manifolds,” Uspekhi Mat. Nauk.,20, No. 6, 3–12 (1965).
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