The equilibrium $$\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}$$ can be influenced by changes in the pH of the medium, according to Le Chatelier's principle. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

In this case:

$$\mathrm{Cr}_2 \mathrm{O}_7^{2-}$$ is dichromate, which exists more prominently in acidic conditions. On the other hand, $$\mathrm{CrO}_4^{2-}$$ is chromate, which is favored in basic conditions. When the medium is basic, hydrogen ion concentration decreases, leading to the formation of more chromate ions ($$\mathrm{CrO}_4^{2-}$$).

Thus, in a basic medium, the reaction shifts to the right, resulting in the formation of $$2 \mathrm{CrO}_4^{2-}$$ from $$\mathrm{Cr}_2 \mathrm{O}_7^{2-}$$.

Therefore, the correct option is:

Option B: a basic medium