Canonical Dimension of (semi-)spinor Groups of Small Ranks

Abstract

We show that the canonical dimension cd Spin2n+1 of the spinor group Spin2n+1 has an inductive upper bound given by n + cd Spin2n−1. Using this bound, we determine the precise value of cd Spinn for all n ≤ 16 (previously known for n ≤ 10). We also obtain an upper bound for the canonical dimension of the semi-spinor group cd Spinn in terms of cd Spinn−2. This bound determines cd Spin ∼ n for n ≤ 16; for any n, assuming a conjecture on the precise value of cd Spinn−2, this bound determines cd Spinn .