A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2

DOI10.1007/BF01457086zbMath0489.17008MaRDI QIDQ1166600

Alex J. Feingold, Igor B. Frenkel

Publication date: 1983

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163734

zbMATH Keywords

Siegel modular formsconstructionSaito-Kurokawa conjectureroot multiplicitieslifting of invariant charactersproduct expansion for theta functionsimplest hyperbolic Kac-Moody algebraWeyl-Kac denominator formula

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Theta series; Weil representation; theta correspondences (11F27)

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Cites Work

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• Modular descent and the Saito-Kurokawa conjecture
• On the Saito-Kurokawa lifting
• Root systems of hyperbolic type
• Realization of the basic representations of the Euclidean Lie algebras
• Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
• Basic representations of affine Lie algebras and dual resonance models
• An arithmetic of Hermitian modular forms of degree two
• Infinite-dimensional Lie algebras and Dedekind's \(\eta\)-function
• Lie algebra homology and the Macdonald-Kac formulas
• Root systems and elliptic curves
• Lie algebraic approaches to classical partition identities
• Construction of the affine Lie algebra \(A^{(1)}_1\)
• The Weyl-Kac character formula and power series identities
• Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
• Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two
• Über eine Spezialschar von Modulformen zweiten Grades. II, III. (On a Spezialschar of modular forms of second degree. II, III)
• Affine root systems and Dedekind's \(\eta\)-function
• Zur analytischen Theorie der Grenzkreisgruppen. II. Divisorentheorie der automorphen Formen komplexer Dimension
• Lie Algebra Multiplicities
• A Hyperbolic GCM Lie Algebra and the Fibonacci Numbers
• Spinor representations of affine Lie algebras
• Affine Lie algebras and Hecke modular forms
• Tensor products of certain modules for the generalized cartan matrix lie algebra
• On defining relations of certain infinite-dimensional Lie algebras
• EULER PRODUCTS CORRESPONDING TO SIEGEL MODULAR FORMS OF GENUS 2
• On Siegel Modular Forms of Genus Two