Siegel automorphic form corrections of some Lorentzian Kac-Moody lie algebras

American Journal of Mathematics

Volumn 119, Issue 1, 1997, Pages 181-224

  Gritsenko, Valeri A ^a   Nikulin, Viacheslav V ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

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EID: 0000672156     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. R. E. Borcherds, Generalized Kac-Moody algebras, J. Algebra 115 (1988), 501-512.
2. _, The monster Lie algebra, Adv. Math. 83 (1990), 30-47.
3. _, Central extensions of generalized Kac-Moody algebras, J. Algebra 140 (1991), 330-335.
4. _, The monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 (1992), 405-444.
5. _, Sporadic groups and string theory Proc. European Congress Math., 1992, Progr. Math., vol. 119, Birkhaüser, Boston, MA, 1994, pp. 411-421.
6. s+2,2(R) and infinite products, Invent. Math. 120 (1995), 161-213.
7. _, The moduli space of Enriques surfaces and the fake monster Lie superalgebra, preprint, 1994.
8. [EZ] M. Eichler and D. Zagier, The Theory of Jacobi Forms, Progr. Math., vol. 55, Birkhäuser, Boston, MA, 1985.
9. [F] E. Freitag, Siegelsche Modulfunktionen, Springer-Verlag, New York, 1983.
10. V. A. Gritsenko, Jacobi functions of n-variables, Zap. Nauchn. Sem. Leningrad. Ofdel. Mat. Inst. Steklov. 168 (1988), 32-45 (Russian); English transl., J. Soviet Math. 53 (1991), 243-252.
11. V. A. Gritsenko, Jacobi functions of n-variables, Zap. Nauchn. Sem. Leningrad. Ofdel. Mat. Inst. Steklov. 168 (1988), 32-45 (Russian); English transl., J. Soviet Math. 53 (1991), 243-252.
12. _, Modular forms and moduli spaces of abelian and K3 surfaces, Algebra i Analiz 6 (1994), 65-102 (Russian); English transl., Petersburg Math. J. 6 (1995), 1179-1208.
13. _, Modular forms and moduli spaces of abelian and K3 surfaces, Algebra i Analiz 6 (1994), 65-102 (Russian); English transl., Petersburg Math. J. 6 (1995), 1179-1208.
14. _, Irrationality of the moduli spaces of polarized abelian surfaces, Internat. Math. Res. Notices 6 (1994), 235-243.
15. _, Modulformen zur Paramodulgruppe und Moculräume der Abelschen Varietäten, Math. Gottingensis, Heft 12, SFB 170 "Geometrie und Analysis," 1995, pp. 1-89.
16. [GH] V. Gritsenko and K. Hulek, Minimal Siegel modular threefolds, Prépublication de l'Institut Fourier, 312 (1995), 1-28.
17. V. A. Gritsenko and V. V. Nikulin, Siegel automorphic form correction of a Lorentzian Kac-Moody algebra, C. R. Acad. Sci. Paris Sér. A-B 321 (1995), 1151-1156.
18. _, The Igusa modular forms and "the simplest" Lorentzian Kac-Moody algebras, Matem. Sbornik 187 (1996), no. 11.
19. _, K3 surfaces, Lorentzian Kac-Moody algebras and mirror symmetry, Math. Res. Let. 3 (1996), 1-19.
20. [HM] J. A. Harvey and G. Moore, Algebras, BPS states, and strings, EFI-95-64, hep-th/9510182.
21. V. Kac, Lie superalgebras, Adv. Math. 26 (1977), 8-96.
22. _, Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula, Adv. Math. 30 (1978), 85-136.
23. _, Infinite Dimensional Lie Algebras Cambridge University Press, New York, 1990.
24. [Kaw] T. Kawai, N = 2 Heterotic string threshold correction, K3 surfaces and generalized Kac-Moody algebra, INS-Rep-1128, hep-th/9512046.
25. H. Maass, Die Multiplikatorsysteme zur Siegelschen Modulgruppe, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II Nr 11 (1964), 125-135.
26. _, Über einer Spezialschar von Modulformen zweiten Grades I, Invent. Math. 52 (1979), 95-104; II, Invent. Math. 53 (1979), 249-253; III, Invent. Math. 53 (1979), 255-265.
27. _, Über einer Spezialschar von Modulformen zweiten Grades I, Invent. Math. 52 (1979), 95-104; II, Invent. Math. 53 (1979), 249-253; III, Invent. Math. 53 (1979), 255-265.
28. _, Über einer Spezialschar von Modulformen zweiten Grades I, Invent. Math. 52 (1979), 95-104; II, Invent. Math. 53 (1979), 249-253; III, Invent. Math. 53 (1979), 255-265.
29. _, Über ein Analogon zur Vermutung von Saito-Kurokawa, Invent. Math. 60 (1980), 85-104.
30. [Mo] R. V. Moody, A new class of Lie algebras, J. Algebra 10 (1968), 211-230.
31. V. V. Nikulin, On arithmetic groups generated by reflections in Lobachevsky spaces, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 637-669 (Russian); English transl., Math. USSR-Izv. 16 (1981), 573-601.
32. V. V. Nikulin, On arithmetic groups generated by reflections in Lobachevsky spaces, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 637-669 (Russian); English transl., Math. USSR-Izv. 16 (1981), 573-601.
33. _, On the classification of arithmetic groups generated by reflections in Lobachevsky spaces, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), 113-142 (Russian); English transl., Math. USSR-Izv. 18 (1982), 99-123.
34. _, On the classification of arithmetic groups generated by reflections in Lobachevsky spaces, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), 113-142 (Russian); English transl., Math. USSR-Izv. 18 (1982), 99-123.
35. _, Surfaces of type K3 with finite automorphism group and Picard group of rank three, Proc. Steklov Inst. Math. 165 (1984), 113-142 (Russian); English transl., Trudy Mat. Inst. Steklov 3 (1985), pp. 131-155.
36. _, Surfaces of type K3 with finite automorphism group and Picard group of rank three, Proc. Steklov Inst. Math. 165 (1984), 113-142 (Russian); English transl., Trudy Mat. Inst. Steklov 3 (1985), pp. 131-155.
37. _, A lecture on Kac-Moody Lie algebras of the arithmetic type, preprint, 1995.
38. _, Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac-Moody Lie algebras, Duke e-prints alg-geom/9503003, Russian Acad. Sci. Izv. Math. (to appear).
39. _, The remark on discriminants of K3 surfaces moduli as sets of zeros of automorphic forms, Duke e-prints alg-geom/9512018.
40. [R] U. Ray, A character formula for generalized Kac-Moody superalgebras, J. Algebra 177 (1995), 154-163.