Irreducible components of two-row Springer fibers and Nakajima quiver varieties

Abstract

We give an explicit description of the irreducible components of two-row Springer fibers in type A as closed subvarieties in certain Nakajima quiver varieties in terms of quiver representations. By taking invariants under a variety automorphism, we obtain an explicit algebraic description of the irreducible components of two-row Springer fibers of classical type. As a consequence, we discover relations on isotropic flags that describe the irreducible components.

38 pages. v3: Not intended for publication; we would like to thank Dongkwan Kim for pointing out that the second goal of this paper can be obtained more efficiently without using the fixed-point subvarieties. This manuscript has therefore been split into the two preprints arXiv:2009.08778 and arXiv:2011.13138