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Super Theta Vectors and Super Quantum Theta Operators

  • Kim, Hoil (Department of Mathematics and Institute for Mathematical Convergence, Kyungpook National University)
  • Received : 2019.03.20
  • Accepted : 2019.06.05
  • Published : 2019.09.23

Abstract

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin's result on bosonic operators, and the author's previous result on fermionic operators.

Keywords

super theta vectors;quantum theta operators;super Heisenberg group

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. M. Bergvelt and J. Rabin, Supercurves, their Jacobians, and super KP equations, Duke Math. J., 98(1)(1999), 1-57. https://doi.org/10.1215/S0012-7094-99-09801-0
  2. A. Connes, M. Douglas and A. Schwarz, Noncommutative geometry and matrix theory, J. High Energy Phys., JHEP 9802(1998), 003, 35 pp.
  3. H. Kim, Quantum super theta vectors and theta functions, Kyungpook Math. J., 56(1)(2016), 249-256. https://doi.org/10.5666/KMJ.2016.56.1.249
  4. Y. Manin, Theta functions, quantum tori and Heisenberg Groups, Lett. Math. Phys., 56(3)(2001), 295-320. https://doi.org/10.1023/A:1017909525397
  5. Y. Manin, Functional equations for quantum theta functions, Publ. Res. Inst. Math. Sci., 40(3)(2004), 605-624.
  6. D. Mumford (with M. Nori and P. Norman), Tata lectures on theta III, Progress in Math. 97, Birkhauser, Boston, 1991.
  7. M. Rieffel, Projective modules over higher dimensional noncommutative tori, Canad. J. Math., 40(2)(1988), 257-338. https://doi.org/10.4153/CJM-1988-012-9
  8. A. Schwarz, Theta functions on noncommutative tori, Lett. Math. Phys., 58(2001), 81-90. https://doi.org/10.1023/A:1012515417396
  9. Y. Tsuchimoto, On super theta functions, J. Math. Kyoto Univ., 34(3)(1994), 641-694. https://doi.org/10.1215/kjm/1250518937
  10. A. Tyurin, Quantization and \theta functions", arXiv:math/9904046.