Quantum Super Theta Vectors and Theta Functions

  • Kim, Hoil
  • Received : 2016.01.18
  • Accepted : 2016.02.05
  • Published : 2016.03.23


There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.


theta functions;theta vectors;quantum theta functions;super torus


  1. C. Ee, H. Kim and H. Nakajima, Noncommutative superspace and super Heisenberg group, JHEP, 0804:004(2008).
  2. C. Ee, H. Kim and H. Nakajima, Noncommutative supertori in two dimensions, JHEP, 0808:058(2008).
  3. A. Connes, M. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: Compactification on tori, JHEP, 9802:003(1998).
  4. Y. Manin, Functional equations for quantum theta functions, Publ. Res. Inst. Math. Sci. Kyoto, 40(3)(2004), 605-624.
  5. Y. Manin, Theta functions, quantum tori and Heisenberg Groups, Lett. Math. Phys., 56(3)(2001), 295-320.
  6. D. Mumford (with M. Nori and P. Norman), Tata Lectures on Theta III, Progress in Math., Vol. 97, Birkhauser, 1991.
  7. D. Quillen, Superconnections and the Chern character, Topology, 24(1)(1985), 89-95.
  8. M. Rieffel, Projective modules over higher dimensional noncommutative tori, Can. J. Math., 40(2)(1988), 257-338.
  9. A. Schwarz, Theta functions on non-commutative tori, Lett. Math. Phys., 58(2001), 81-90.


Supported by : National Research Foundation of Korea (NRF)