Related papers: Irreducible components of two-row Springer fibers …

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…

The description of the intersections of components of a Springer fiber is a very complex problem. Up to now only two cases have been described completely. The complete picture for the hook case has been obtained by N. Spaltenstein and J.A.…

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N^2=0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these…

We explain an elementary topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group and component…

Webs and Springer fibers are separately important objects in representation theory: webs give a diagrammatic calculus for tensor invariants of $\mathfrak{sl}_k$, and the cohomology group of Springer fibers can be used to construct the…

We describe the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl_n(C) as iterated bundles of flag manifolds and Grassmannians. We then relate the topology (in particular, the intersection homology…

This paper is a subsequent paper of math.RT/0607673. Here we consider the irreducible components of Springer fibres (or orbital varieties) for two-column case in GL}_n. We describe the intersection of two irreducible components, and…

We study in detail two row Springer fibres of even orthogonal type from an algebraic as well as topological point of view. We show that the irreducible components and their pairwise intersections are iterated P^1-bundles. Using results of…

Let $u\in\mathrm{End}(\mathbb{C}^n)$ be nilpotent. The variety of $u$-stable complete flags is called the Springer fiber over $u$. Its irreducible components are parameterized by a set of standard Young tableaux. The Richardson (resp.…

Let $u$ be a nilpotent endomorphism of a finite dimensional $\mathbb{C}$-vector space. The set ${\mathcal F}_u$ of $u$-stable complete flags is a projective algebraic variety called a Springer fiber. Its irreducible components are…

For a fixed 2-block Springer fiber, we describe the structure of its irreducible components and their relation to the Bialynicki-Birula paving, following work of Fung. That is, we consider the space of complete flags in C^n preserved by a…

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

We define a new family of algebraic varieties, called exotic Spaltenstein varieties. These generalise the notion of Spaltenstein varieties (which are the partial flag analogues to classical Springer fibres) to the case of exotic Springer…

For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…

The $\Delta$-Springer fibers $Y_{n,\lambda,s}$, introduced by Levinson, Woo, and the second author, generalize Springer fibers for $\mathrm{GL}_n(\mathbb{C})$ and give a geometric interpretation of the of the Delta Conjecture from algebraic…

We develop a new general method for computing the decomposition type of the normal bundle to a projective rational curve. This method is then used to detect and explain an example of a Hilbert scheme that parametrizes all the rational…

It is a remarkable theorem by Maffei--Nakajima that the Slodowy variety, which is a subvariety of the resolution of the nilpotent cone, can be realized as a Nakajima quiver variety of type A. However, the isomorphism is rather implicit as…

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan basis and consider the standard torus relative to this. We deal with the problem to describe the flags fixed by the torus which belong to a given component of the…

Let ${\mathcal B}_u$ be the Springer fiber over a nilpotent endomorphism $u\in End(\mathbb{C}^n)$. Let $J(u)$ be the Jordan form of $u$ regarded as a partition of $n$. The irreducible components of ${\mathcal B}_u$ are all of the same…

Springer fibers are a family of subvarieties of the flag variety parametrized by nilpotent matrices that are important in geometric representation theory and whose geometry encodes deep combinatorics. Two-row Springer fibers, which…