BASIC SPIN REPRESENTATIONS OF ALTERNATING GROUPS, GOW LATTICES, AND BARNES-WALL LATTICES
Fam Khyu T'ep · Sbornik Mathematics · 1994
In a recent paper, R. Gow showed that in certain cases the basic spin representations of the group (of degree ) can be rational. In such cases, the -invariant lattices in the corresponding rational module have many interesting properties. In the present paper all possibilities are found for the groups . Also, a conjecture of Gow is proved: For , , there is among the -invariant lattices the even unimodular Barnes-Wall lattice . At the same time, the rationality of the basic spin representation of and the reducibility of as a -module are proved.Bibliography: 21 titles.