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ON COMMUTING ORDINARY DIFFERENTIAL OPERATORS WITH POLYNOMIAL COEFFICIENTS CORRESPONDING TO SPECTRAL CURVES OF GENUS TWO

  • Davletshina, Valentina N. ;
  • Mironov, Andrey E.
  • Received : 2016.08.17
  • Accepted : 2016.10.25
  • Published : 2017.09.30

Abstract

The group of automorphisms of the first Weyl algebra acts on commuting ordinary differential operators with polynomial coefficient. In this paper we prove that for fixed generic spectral curve of genus two the set of orbits is infinite.

Keywords

commuting ordinary differential operators;the first Weyl algebra

References

  1. V. N. Davletshina, Commuting differential operators of rank two with trigonometric coefficients, Sib. Math. J. 56 (2015), no. 3, 405-410. https://doi.org/10.1134/S0037446615030040
  2. J. Dixmier, Sur les algebres de Weyl, Bull. Soc. Math. France 96 (1968), 209-242.
  3. I. M. Krichever, Commutative rings of ordinary linear differential operators, Functional Anal. Appl. 12 (1978), no. 3, 175-185. https://doi.org/10.1007/BF01681429
  4. I. M. Krichever and S. P. Novikov, Holomorphic bundles over algebraic curves and nonlinear equations, Russian Math. Surveys 35 (1980), no. 6, 47-68.
  5. A. E. Mironov, Self-adjoint commuting ordinary differential operators, Invent. Math. 197 (2014), no. 2, 417-431. https://doi.org/10.1007/s00222-013-0486-8
  6. A. E. Mironov, Periodic and rapid decay rank two self-adjoint commuting differential operators, Topology, geometry, integrable systems, and mathematical physics, 309-321, Amer. Math. Soc. Transl. Ser. 2, 234, Amer. Math. Soc., Providence, RI, 2014.
  7. A. E. Mironov and A. B. Zheglov, Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra, Int. Math. Res. Not. 2016 (2016), no. 10, 2974-2993. https://doi.org/10.1093/imrn/rnv218
  8. O. I. Mokhov, Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients, Topology, geometry, integrable systems, and mathematical physics, 323-336, Amer. Math. Soc. Transl. Ser. 2, 234, Amer. Math. Soc., Providence, RI, 2014.
  9. V. S. Oganesyan, Commuting differential operators of rank 2 and arbitrary genus g with polynomial coefficients, Russian Math. Surveys 70 (2015), no. 1, 165-167. https://doi.org/10.1070/RM2015v070n01ABEH004939
  10. V. S. Oganesyan, Commuting differential operators of rank 2 with polynomial coefficients, Functional Anal. Appl. 50 (2016), no. 1, 54-61. https://doi.org/10.1007/s10688-016-0128-1

Acknowledgement

Supported by : Russian Foundation for Basic Research