Rost Multipliers of Lifted Kronecker Tensor Products

Abstract

We extend techniques employed by Garibaldi to construct various new injections involving the half-spin group, $\mathbf{HSpin}$, induced by lifting the Kronecker tensor product to simply connected groups. We calculate the Rost multipliers of the maps we have constructed. Furthermore, we utilize our new map ${\mathbf{PSp}}_{2n}\times {\mathbf{PSp}}_{2m}\hookrightarrow {\mathbf{HSpin}}_{4nm}$ to describe the structure of the normalized degree three cohomological invariants of ${\mathbf{HSpin}}_{4n}$.