Normalizers of elementary overgroups of $\mathrm{Ep}(2,A)$

Let $A$ be an involution ring, $e_1,\dots,e_n$ be a full system of hermitian idempotents in $A$, every $e_i$ generates $A$ as a two-sided ideal, and $2\in A^*$. In this paper we calculate normalizers of groups $\mathrm{Ep}(2,A)\cdot\mathrm E(2,A,I)$ under natural assumptions on $A$, where $\mathrm{Ep}(2,A)$ denotes the elementary symplectic group, $\mathrm E(2,A,I)$ elementary subgroups of level $I$.