To construct the convolution product for two ($G(O)$-equivariant) perverse sheaves $\mathcal{F}, \mathcal{G}$ on affine grassmanian, the first thing we need to compute is $^PH^0(\mathcal{F} \boxtimes^L \mathcal{G})$.
Suppose $\mathcal{F}$ and $\mathcal{G}$ are the intersection sheaves correspond to stratum $Gr_\mu$ and $Gr_\lambda$ respectively, how do we compute $^PH^0(\mathcal{F} \boxtimes^L \mathcal{G})$ explicitly?
