Invariant hermitian lattices in the steinberg module and their isometry groups

摘要

The invariant Hermitian lattices in the Steinberg module of SL2(q) are described. These lattices are connected with generalized quadratic residue codes over a field of four elements. The isometry groups of in-variant lattices are calculated. In particular, lbdimensional unimodular lattices over Eisenstein numbers with minimum norm 3 and automor- phism group Z6x PSp6(3) are obtained.