Chevalley groups of types $B_n$, $C_n$, $D_n$ over certain fields do not possess the $R_{\infty}$-property

Abstract

Let $F$ be an algebraically closed field of zero characteristic. If the transcendence degree of $F$ over $\mathbb{Q}$ is finite, then all Chevalley groups over $F$ are known to possess the $R_{\infty}$-property. If the transcendence degree of $F$ over $\mathbb{Q}$ is infinite, then Chevalley groups of type $A_n$ over $F$ do not possess the $R_{\infty}$-property. In the present paper we consider Chevalley groups of classical series $B_n$, $C_n$, $D_n$ over $F$ in the case when the transcendence degree of $F$ over $\mathbb{Q}$ is infinite, and prove that such groups do not possess the $R_{\infty}$-property.