zbMATH — the first resource for mathematics

Singular holomorphic representations and singular modular forms. (English) Zbl 0466.32017

32N10 Automorphic forms in several complex variables
17B15 Representations of Lie algebras and Lie superalgebras, analytic theory
32M05 Complex Lie groups, group actions on complex spaces
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
11F27 Theta series; Weil representation; theta correspondences
17B35 Universal enveloping (super)algebras
Full Text: DOI EuDML
[1] Ash, A., Mumford, D., Rapaport, M., Tai, Y.S.: Smooth compactification of locally symmetric varieties. Brookline: Mathematical Science Press 1975 · Zbl 0334.14007
[2] Braun, H., Koecher, M.: Jordan Algebren. Berlin, Heidelberg, New York: Springer 1966
[3] Freitag, E.: Holomorphe Differentialformen zu Kongruenzgruppen der Siegelschen Modulgruppe. Invent Math.30, 181-196 (1975) · Zbl 0314.32017 · doi:10.1007/BF01425508
[4] Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962. · Zbl 0111.18101
[5] Jakobsen, H.P.: Intertwining differential operators forMp(n, ?) and SU(n, n). Trans. A.M.S.246, 311-337 (1978) · Zbl 0403.22010
[6] Jakobsen, H.P., Vergne, M.: Restrictions and expansions of holomorphic representations. J. Functional Analysis34, 29-53 (1979) · Zbl 0433.22011 · doi:10.1016/0022-1236(79)90023-5
[7] Konstant, B.: Verma modules and the existence of quasi-invariant differential operators. In: Noncommutative harmonic analysis. Lecture Notes in Mathematics, Vol. 466. Berlin, Heidelberg, New York: Springer 1975
[8] Maass, H.: Siegel’s modular forms and Dirichlet series. In: Lecture Notes in Mathematics, Vol.216. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0224.10028
[9] Mars, J.G.M.: Les nombres de Tamagawa de certains groupes exceptionnels. Bull. Math. Soc. France94, 97-140 (1966) · Zbl 0146.04601
[10] Resnikoff, H.L.: Automorphic forms of singular weight are singular forms. Math. Ann.215, 173-193 (1975) · Zbl 0304.32019 · doi:10.1007/BF01432694
[11] Resnikoff, H.L.: On a class of linear differential equations for automorphic forms in several complex variables. Am. J. Math.95, 321-332 (1973) · Zbl 0276.32023 · doi:10.2307/2373788
[12] Springer, T.: Jordan algebras and algebraic groups. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0259.17003
[13] Vergne, M., Rossi, H.: Analytic continuation of holomorphic discrete series. Acta Math.136 1-59 (1976) · Zbl 0356.32020 · doi:10.1007/BF02392042
[14] Wolf, J.: Fine structure of Hermitian symmetric spaces. In: Symmetric spaces. Short Lectures, pp. 271-357. New York: Dekker 1972 · Zbl 0257.32014
[15] Wallach, N.: Analytic continuation of the discrete series. II. Trans. A.M.S.251, 19-37 (1979) · Zbl 0419.22018 · doi:10.1090/S0002-9947-79-99965-3
[16] Borel, A.: Reduction theory for arithmetic groups. Proc. Symp. Pure Math.9, 20-25 (1966) · Zbl 0213.47201
[17] Weil, A.: Ad?les and algebraic groups. Lecture notes, Institute for Advanced Study. Princeton (1961)
[18] Schmid, W.: Die Randwerte holomorpher Funktionen auf Hermitesch symmetrisch?n R?umen. Invent Math.9, 61-80 (1969) · Zbl 0219.32013 · doi:10.1007/BF01389889
[19] Freitag, E.: K?per der Siegelschen Modulfunktionen. Abh. Math. Sem. Univ. Hamburg47, 25-41 (1978) · Zbl 0402.10028 · doi:10.1007/BF02941350
[20] Freitag, E.: Thetareihen mit harmonischen Koeffizienten zur Siegelschen Modulgruppe. Math Ann.254, 27-51 (1980) · Zbl 0445.10022 · doi:10.1007/BF01457884
[21] Howe, R.: Automorphic forms of low rank (preprint) (1980)
[22] Harish-Chandra: Discrete series for semisimple Lie groups II. Acta Math.116, 1-111 (1966) · Zbl 0199.20102 · doi:10.1007/BF02392813
[23] Maass, H.: Siegel’s modular forms and dirichlet series. Lecture Notes in Mathematics. Vol. 216 Berlin, Heidelberg, New York: Springer 1971 · Zbl 0224.10028
[24] Jakobsen, H.P.: On singular holomorphic representations. Invent Math.62, 67-78 (1980) · Zbl 0466.22016 · doi:10.1007/BF01391663
[25] Jakobsen, H.P.: The last possible place of unitarity for certain highest weight modules. (preprint) (1980)
[26] Enright, T., Parthasarathy, R.: A proof of a conjecture of Kashiwara and Vergne (preprint) (1980) · Zbl 0492.22012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.