Papers by Richard Borcherds

Back to Dave Benson's Preprint Archive

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Classification of positive definite lattices

Preprint.

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Problems in moonshine

Preprint.

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Quantum vertex algebras

Preprint, 1999.

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Reflection groups of Lorentzian lattices

Duke Math. J. 104 (2000), 319-366.

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Coxeter groups, Lorentzian lattices, and K3 surfaces

Internat. Math. Res. Notices 19 (1998), 1011-1031.

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What is moonshine?

Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998). Doc. Math. 1998, Extra Vol. I, 607-615.

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What is a vertex algebra?

Unpublished 1997 Arbeitstagung talk.

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Automorphic forms and Lie algebras

Current Developments in mathematics 1996, International Press 1998.

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The fake monster formal group

Duke Math J. Vol 100 No. 1 (1999), 139-165.

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The Gross-Kohnen-Zagier theorem in higher dimensions

Duke Math. J. 97 (1999), no. 2, 219-233.

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Vertex algebras

Topological field theory, primitive forms and related topics (Kyoto, 1996), 35-77, Progr. Math., 160, Birkhäuser Boston, Boston, MA, 1998.

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An automorphic form related to cubic surfaces

Unpublished note, 1998.

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Automorphic forms with singularities on Grassmannians

Invent. Math. 132, 491-562 (1998).

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Modular moonshine III

Duke Math. J. 93 (1998), no. 1, 129-154.

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The moduli space of Enriques surfaces and the fake monster Lie superalgebra

Topology 35 (1996), 699-710.

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Automorphic forms on O_s+2,2(R)⁺ and generalized Kac-Moody algebras

Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 744-752, Birkhäuser, Basel, 1995.

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Automorphic forms on O_s+2,2(R) and infinite products

Invent. Math. 120 (1995), 161-213.

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A characterization of generalized Kac-Moody algebras

J. Algebra 174, 1073-1079 (1995).

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Sporadic groups and string theory

First E. C. M., Vol. I (Paris, 1992), 411-421, Progr. Math., 119, Birkhäuser, Basel, 1994.

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Monstrous moonshine and monstrous Lie superalgebras

Invent. Math. 109 (1992), 405-444.

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Introduction to the monster Lie algebra

(expository) ``Groups, combinatorics, and geometry, Durham 1990'', p. 99-107, L.M.S. lecture notes in mathematics 165, C.U.P. 1992, edited by M.W.Liebeck and J.Saxl.

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Central extensions of generalized Kac-Moody algebras

J. Algebra 140 (1991), 330-335.

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The monster Lie algebra

Adv. Math. 83 (1990), 30-47.

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Lattices like the Leech lattice

J. Algebra 130 (1990), 219-234.

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The 24-dimensional odd unimodular lattices

Sphere packings, lattices, and groups, by J. H. Conway and N. J. A. Sloane, chapter 17, pp. 421-430.

(This does not include the table of such lattices, which is available as a separate html file table-4.html above)

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Generalized Kac-Moody algebras

J. Algebra 115 (1988), 501-512.

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Automorphism groups of Lorentzian lattices

J. Algebra 111 (1987) 133-153.

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Vertex algebras, Kac-Moody algebras and the monster

Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 3068-3071.

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The Leech lattice

Proc. Royal Soc. London A398 (1985) 365-376.

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The Leech lattice and other lattices

Ph. D. thesis (Cambridge, 1985).