A Witt’s theorem for unimodular lattices
Y. C. Lee · Pacific Journal of Mathematics · 1979
Let K be a dyadic local field, o its ring of integers, L a regular unimodular lattice over o.If x and y are vectors in L, we ask for necessary and sufficient conditions to map x isometrically to y. Trojan and James obtain conditions via a T-invariant when o is 2-adic.Hsia uses characteristic sets and G-invariants for vectors and he solves the problem when o is dyadic in general.We define here a new numerical invariant, the degree of a vector, which reflects more on the structure of L and the relationship between x, y and L. The Witt conditions will be stated in terms of this degree invariant.