I am trying to calculate explicitly a certain simple exotic sheaf (a simple object of the heart of the exotic t-structure on the Springer resolution, which is defined in Theorem 1.5.1 of Bezrukavnikov-Mirkovic) for ${\rm Sp}(6)$. I am trying to use for this purpose Proposition 1.2 in Achar's notes.
My questions are: do the simple objects in Theorem 1.3 in Achar lie in the heart of the exotic t-structure of Bezrukavnikov-Mirkovic? What is the relation between (simple) exotic sheaves in Achar and in Bezrukavnikov-Mirkovic?
Update: Apparently what Achar calls "simple exotic sheaves" are known by the name "simple perversely exotic sheaves" in Section 6.2.2 of Bezrukavnikov-Mirkovic. I am still interested what is the relation between simple exotic sheaves in Bezrukavnikov-Mirkovic and simple perversely exotic sheaves in Bezrukavnikov-Mirkovic, can one be calculated if we know the other?
