Isometric structure ($(V,Q,T)$)

An isometric structure consists of a finite-dimensional vector space $V$, a nonsingular symmetric bilinear form $Q$, and a $Q$-isometry $T$ with the required nondegeneracy at $\pm 1$. Metabolic isometric structures are quotiented out to form ${\mathcal{W}}_F$.

The Witt group of isometric structures identifies two isometric structures when their orthogonal difference is metabolic.

For an irreducible symmetric Laurent polynomial $\delta$, the primary component isfor sufficiently large $N$. Distinct symmetric primary components are orthogonal, so restriction defines a projection ${\mathcal{W}}_F\to {\mathcal{W}}_F^{\delta }$.