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Let $G$ be a complex reductive group, $T$ be a maximal torus of $G$, $B$ be aBorel subgroup of $G$ containing $T$, $W$ be the Weyl group of $G$ with respectto $T$. To each element $w$ of $W$ one can associate the Schubert subvariety$X_w$ of the flag variety $G/B$, the tangent cone to $X_w$ at the identitypoint $p$ considered as a subcheme of the tangent space $T_p(G/B)$, and thereduced tangent cone to $X_w$ at $p$ considered as a subvariety of $T_p(G/B)$.Let $w_1$, $w_2$ be distinct involutions in $W$. We prove that if $G$ is oftype $B_n$ or $C_n$, then the tangent cones corresponding to $w_1$ and $w_2$are distinct. We also prove that if $G$ is of type $A_n$ or $C_n$, then thereduced tangent cones corresponding to $w_1$ and $w_2$ are distinct.

Tangent cones to Schubert varieties in types $A_n$, $B_n$ and $C_n$