Stability of special instanton bundles on 𝑃²ⁿ⁺¹

We prove that the special instanton bundles of rank 2 n 2n on P 2 n + 1 ( C ) {\mathbb {P}^{2n + 1}}(\mathbb {C}) with a symplectic structure studied by Spindler and Trautmann are stable in the sense of Mumford-Takemoto. This implies that the generic special instanton bundle is stable. Moreover all instanton bundles on P 5 {\mathbb {P}^5} are stable. We get also the stability of other related vector bundles.