Abstract
We give a classification of modules with Gel’fand-Kirillov dimensionn and multiplicity one over the Weyl algebran A n.
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References
R. E. Block, “Classification of the irreducible representations of sl (2, ℂ),”Bull. Amer. Math. Soc.,1, No. 1, 247–250 (1979).
R. E. Block, “The irreducible representations of the Lie algebra sl (2) and of the Weyl algebra,”Adv. Math.,39, 69–110 (1981).
V. V. Bavula, “Generalized Weyl algebras and their representations,”Algebra Anal.,4, Issue 1, 74–95 (1992).
V. V. Bavula, “SimpleD[X, Y; σ,a-modules,”Ukr. Mat. Zh.,44, No. 12, 1628–1644 (1992).
J. E. Björk,Rings of Differential Operators, North-Holland, Amsterdam 1979.
I. N. Bernshtein, “Modules over a ring of differential operators. Investigation of fundamental solutions of equations with constant coefficients,”Funkts. Anal Prilozhen.,5, No 2, 1–16 (1971).
V. V. Bavula, “Extreme modules over the Weyl algebraA n,” in:Abstracts of the 14th All-Union School on Operators in Functional Spaces [in Russian], Nizhnii Novgorod (1991), p. 16.
V. V. Bavula,Generalized Weyl Algebras, Preprint, Bielefeld 1994.
J. T. Stafford, “Non-holonomic modules over Weyl algebras and enveloping algebras,”Invent. Math., 92–93, 619–638 (1985).
J. E. Roos, “Sur les foncteurs derives de lim. Applications,”C. R. Acad. Sci.,252, No. 24, 3702–3704 (1961).
P. Gabriel and R. Rentschler, “Sur la dimension des anneaux et ensembles ordonnes,”C. R. Acad. Sci.,265, 712–715 (1967).
J. Dixmier, “Sur les algebres de Weyl,”Bull. Soc. Math. France,96, 209–242 (1968).
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Bavula, V.V. Classification of modules of dimension n and multiplicity one over the weyl algebraA n . Ukr Math J 48, 643–651 (1996). https://doi.org/10.1007/BF02384223
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DOI: https://doi.org/10.1007/BF02384223