Hitchin systems at low genera

Journal of Mathematical Physics

Volumn 41, Issue 7, 2000, Pages 4695-4712

  Gawȩdzki, Krzysztof ^a   Tran Ngoc Bich, Pascal ^b  

^a CNRS   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034389537     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533372     Document Type: Article

References (25)

1. N. J. Hitchin, "Stable bundles and integrable systems," Duke Math. J. 54, 91 (1987).
2. E. Markman, "Spectral curves and integrable systems," Compositio Mathematica 93, 255 (1994).
3. N. Nekrasov, "Holomorphic bundles and many-body systems," Commun. Math. Phys. 180, 587 (1996).
4. B. Enriquez and V. Rubtsov, "Hitchin systems, higher Gaudin operators and r-matrices," Math. Res. Lett. 3, 343 (1996).
5. F. Falceto and K. Gawȩdzki, "Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe ansatz for the elliptic Hitchin systems," Commun. Math. Phys. 183, 267 (1997).
6. E. Witten, "Quantum field theory and Jones polynomial," Commun. Math. Phys. 121, 351 (1989).
7. E. Verlinde, "Fusion rules and modular transformations in 2D conformal field theory," Nucl. Phys. B 300, 360 (1988).
8. N. J. Hitchin, "Flat connections and geometric quantization," Commun. Math. Phys. 131, 347 (1990).
9. V. G. Knizhnik and A. B. Zamolodchikov, "Current algebra and Wess-Zumino model in two dimensions," Nucl. Phys. B 247, 83 (1984).
10. D. Bernard, "On the Wess-Zumino-Witten models on the torus," Nucl. Phys. B 303, 77 (1988).
11. D. Bernard, "On the Wess-Zumino model on Riemann surfaces," Nucl. Phys. B 309, 145 (1988).
12. K. Gawȩdzki, "Constructive conformal field theory," in Functional Integration, Geometry and Strings, edited by Z. Haba and J. Sobczyk (Birkhäuser, Basel, Boston, Berlin, 1989), pp. 277-302.
13. A. A. Beilinson and V. G. Drinfeld, "Quantization of Hitchin's fibration and Langlands' program," in Algebraic and Geometric Method in Mathematical Physics, Math. Phys. Stud. (Kluwer Academic, Dordrecht, 1996), Vol. 19, p. 3.
14. E. Frenkel, Affine Algebras, Langlands Duality, and Bethe Ansatz, in Proceedings of the XIth International Congress of Mathematical Physics, edited by D. lagolnitzer (International, Boston, 1995), pp. 606-642.
15. P. Etingof and A. Kirillov Jr., "Representations of affine Lie algebras, parabolic differential equations and Lamé functions," Duke Math. J. 74, 585 (1994).
16. F. Falceto and K. Gawȩdzki, "Chern-Simons states at genus one," Commun. Math. Phys. 159, 549 (1994).
17. G. Felder and A. Varchenko, "Integral representations of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations," Int. Math. Res. Not. 5, 221 (1995).
18. G. Felder and C. Wieczerkowski, "Conformal blocks on elliptic curves and the Knizhnik-Zamolodchikov-Bernard equations," Commun. Math. Phys. 176, 113 (1996).
19. M. S. Narasimhan and S. Ramanan, "Moduli of vector bundles on a compact Riemann surface," Ann. Math. 89, 19 (1969).
20. B. van Geemen and E. Previato, "On the Hitchin system," Duke Math. J. 85, 659 (1996).
21. 2 Hitchin integrable system at genus two," Commun. Math. Phys. 196, 641 (1998).
22. B. van Geemen and A. J. de Jong, "On Hitchin's connection," J. Am. Math. Soc. 11, 189 (1998).
23. C. Neumann, "De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur," Crelle 56 (1859).
24. D. Mumford, Tota Lectures on Theta II (Birkhäuser, Basel, 1984).
25. J. Avan and M. Talon, "Poisson structure and integrability of the Neumann-Moser-Uhlenbeck model," Int. J. Mod. Phys. A 5, 4477 (1990).