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The Springer resolution of the nilpotent cone is used to give a geometric construction of the irreducible representations of Weyl groups. Borho and MacPherson obtain the Springer correspondence by applying the decomposition theorem to the Springer resolution, establishing an injective map from the set of irreducible Weyl group representations to simple equivariant perverse sheaves on the nilpotent cone. In this manuscript, we consider a generalization of the Springer resolution using a variety defined by the first author. Our main result shows that in the type A case, applying the decomposition theorem to this map yields all simple perverse sheaves on the nilpotent cone with multiplicity as predicted by Lusztigs generalized Springer correspondence.
In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail using the
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.
One can associate an invariant to a large class of regular codimension two defects of the six dimensional $(0,2)$ SCFT $mathscr{X}[j]$ using the classical Springer correspondence. Such an association allows a simple description of S-duality of associ
This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya, December
We construct a modular generalized Springer correspondence for any classical group, by generalizing to the modular setting various results of Lusztig in the case of characteristic-$0$ coefficients. We determine the cuspidal pairs in all classical typ