Equivariant quantum cohomology of cotangent bundle of $G\mathrm{/}P$

Let $G$ denote a complex semisimple linear algebraic group, $P$ a parabolic subgroup of $G$ and $\mathcal{P}=G\mathrm{/}P$. We identify the quantum multiplication by divisors in $T^{\ast }\mathcal{P}$ in terms of stable basis, which is introduced by Maulik and Okounkov. Using this and the restriction formula for stable basis, we show that the $G\times {\mathbb{C}}^{\ast }$-equivariant quantum multiplication formula in $T^{\ast }\mathcal{P}$ is conjugate to the conjectured formula by Braverman.