SIEGEL AUTOMORPHIC FORM CORRECTIONS OF SOME LORENTZIAN KAC-MOODY LIE-ALGEBRAS

Citation
Va. Gritsenko et Vv. Nikulin, SIEGEL AUTOMORPHIC FORM CORRECTIONS OF SOME LORENTZIAN KAC-MOODY LIE-ALGEBRAS, American journal of mathematics, 119(1), 1997, pp. 181-224
Citations number
35
Categorie Soggetti
Mathematics, General",Mathematics
ISSN journal
00029327
Volume
119
Issue
1
Year of publication
1997
Pages
181 - 224
Database
ISI
SICI code
0002-9327(1997)119:1<181:SAFCOS>2.0.ZU;2-H
Abstract
We find automorphic form corrections which are generalized Lorentzian Kac-Moody superalgebras without odd real simple roots for two elliptic Lorentzian Kac-Moody algebras of rank 3 with a lattice Weyl vector, a nd calculate multiplicities of their simple and arbitrary roots. These Kac-Moody algebras are defined by hyperbolic symmetrized generalized Cartan matrices [GRAPHICS] of rank 3. Both these algebras have ellipti c type (i.e., their Weyl groups have fundamental polyhedra of finite v olume in corresponding hyperbolic spaces) and have a lattice Weyl vect or. The correcting automorphic forms are Siegel modular forms. The for m corresponding to G(1) is the classical Siegel cusp form of weight 5 which is the product of ten even theta-constants. In particular we fin d an infinite product formula for this modular form.