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Published July 2003 | Submitted
Journal Article Open

On the involutions fixing the class of a lattice

Abstract

With any integral lattice Λ in n-dimensional Euclidean space we associate an elementary abelian 2-group I(Λ) whose elements represent parts of the dual lattice that are similar to Λ. There are corresponding involutions on modular forms for which the theta series of Λis an eigenform; previous work has focused on this connection. In the present paper I(Λ) is considered as a quotient of some finite 2-subgroup of O_n(ℝ). We establish upper bounds, depending only on n, for the order of I(Λ), and we study the occurrence of similarities of specific types.

Additional Information

© 2003 Elsevier Science (USA). Received 23 October 2002, Revised 15 November 2002, Available online 16 April 2003.

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