On the cohomology of Fano varieties and the Springer correspondence
  In this paper we compute the cohomology of the Fano varieties of $k$-planes in the smooth complete intersection of two quadrics in $\mathbb{P}^{2g+1}$, using Springer theory for symmetric spaces. 
Tsao-Hsien Chen, Kari Vilonen, and Ting Xue
math.AG math.RT