TY - JOUR

T1 - An E8-approach to the moonshine vertex operator algebra

AU - Shimakura, Hiroki

N1 - Funding Information:
The author was partially supported by Grants-in-Aid for Scientific Research (No. 20549004) and Excellent Young Researcher Overseas Visit Program, Japan Society for the Promotion of Science.

PY - 2011/4

Y1 - 2011/4

N2 - In this article, we study the moonshine vertex operator algebra starting with the tensor product of three copies of the vertex operator algebra V √2E8+, and describe it by the quadratic space over double-struck F sign2 associated to V√2E8 +. Using quadratic spaces and orthogonal groups, we show the transitivity of the automorphism group of the moonshine vertex operator algebra on the set of all full vertex operator subalgebras isomorphic to the tensor product of three copies of V√2E8+, and determine the stabilizer of such a vertex operator subalgebra. Our approach is a vertex operator algebra analogue of 'An E8-approach to the Leech lattice and the Conway group' by Lepowsky and Meurman. Moreover, we find new analogies among the moonshine vertex operator algebra, the Leech lattice and the extended binary Golay code.

AB - In this article, we study the moonshine vertex operator algebra starting with the tensor product of three copies of the vertex operator algebra V √2E8+, and describe it by the quadratic space over double-struck F sign2 associated to V√2E8 +. Using quadratic spaces and orthogonal groups, we show the transitivity of the automorphism group of the moonshine vertex operator algebra on the set of all full vertex operator subalgebras isomorphic to the tensor product of three copies of V√2E8+, and determine the stabilizer of such a vertex operator subalgebra. Our approach is a vertex operator algebra analogue of 'An E8-approach to the Leech lattice and the Conway group' by Lepowsky and Meurman. Moreover, we find new analogies among the moonshine vertex operator algebra, the Leech lattice and the extended binary Golay code.

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U2 - 10.1112/jlms/jdq078

DO - 10.1112/jlms/jdq078

M3 - Article

AN - SCOPUS:79952921561

VL - 83

SP - 493

EP - 516

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 2

ER -