Abstract
If the modular group Γ=SL(2,ℤ) operates in the usual way on complex vector spaces generated by suitably chosen theta constants of level q (i.e. modular forms for the congruence subgroup Γ(q) of Γ), then this operation defines a representation of the group SL(2,ℤ/qℤ). Using this method, we construct all Weil representations of these groups for any prime-power q. It is shown how they depend on the underlying quadratic form of the theta constants and how theta relations can be used to find invariant subspaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
CASSELMAN, W.: On the representations of SL2(k) related to binary quadratic forms. Am.J.Math.94, 810–834 (1972).
KLOOSTERMAN, H.D.: The behaviour of general theta functions under the modular group and the characters of the binary modular congruence groups I, II. Ann. of Math., II.Ser.,47, 317–447 (1946).
NOBS, A., WOLFART, J.: Darstellungen von SL(2,ℤ/pλℤ) und Thetafunktionen I. Math.Z.138, 239–254 (1974).
NOBS, A.: Die irreduziblen Darstellungen der Gruppen SL2(ℤp) I. In Vorbereitung.
NOBS, A., WOLFART, J.: Die irreduziblen Darstellungen der Gruppen SL2(ℤp) II. In Vorbereitung.
SIEGEL, C.L.: A generalization of the Epstein zeta function. Journ.Indian Math.Soc.20, 1–10 (1956).
TANAKA, S.: Irreducible representations of the binary modular congruence groups mod pλ. J. Math. Kyoto Univ.7, 123–132 (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wolfart, J. Darstellungen von SL(2,ℤ/pλℤ) und Thetafunktionen. II. Manuscripta Math 17, 339–362 (1975). https://doi.org/10.1007/BF01170731
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01170731