I recently learned of a result of Brundan describing the centre of the regular block of parabolic category $\mathcal{O}$ for $\mathfrak{gl}\_{n}$ as the cohomology of a corresponding Springer fibre (available [here](http://darkwing.uoregon.edu/~brundan/papers/springernew.pdf)); this is an isomorphism at the level of $\mathbb{C}$-algebras. However, we also have an action of the symmetric group on these cohomology algebras.


*Question*: Is there a way to define an $S\_{n}$-action on the centre of (parabolic) category $\mathcal{O}$ for $\mathfrak{gl}\_{n}$, and in such a way that Brundan's isomorphism becomes a morphism of graded $S\_{n}$-modules? 


Of course, I can simply transport the $S\_{n}$-action in the obvious way but I was looking for a more intrinsic action on the centre that arises from (parabolic) category $\mathcal{O}$ itself. Also, I've had a look at Brundan's paper but it doesn't appear to be discussed there (if I'm being blind then please let me know!)


Thanks in advance.



Springer Action on Centre of Parabolic Category O (after Brundan)
David's comment is correct. This is proven in Section 3 of this paper of Stroppel: <http://arxiv.org/abs/math.RT/0608234>


