相关论文: A unified approach on Springer fibers in the hook,…

We consider the Springer fiber ${\mathcal B}_u$ corresponding to a nilpotent endomorphism $u$ of nilpotent order 2. As a first result, we give a description of the elements of a given component of ${\mathcal B}_u$ which are fixed by the…

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…

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…

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…

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…

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.…

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…

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.…

For $x\in End(K^n)$ satisfying $x^2 = 0$ let $F_x$ be the variety of full flags stable under the action of $x$ (Springer fiber over $x$). The full classification of the components of $F_x$ according to their smoothness was provided in a…

We give an explicit description of the irreducible components of two-row Springer fibers for all classical types using cup diagrams. Cup diagrams can be used to label the irreducible components of two-row Springer fibers. Given a cup…

We prove several new results about the topology of fibers of Gelfand--Zeitlin systems on unitary and orthogonal coadjoint orbits, at the same time finding a unifying framework recovering and shedding light on essentially all known results.…

In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…

This survey paper describes Springer fibers, which are used in one of the earliest examples of a geometric representation. We will compare and contrast them with Schubert varieties, another family of subvarieties of the flag variety that…

We show that the Alexander and Thurston norms are the same for all irreducible Eisenbud-Neumann graph links in homology 3-spheres. These are the links obtained by splicing Seifert links in homology 3-spheres together along tori. By…

The fixed-point index of a homeomorphism of Jordan curves measures the number of fixed-points, with multiplicity, of the extension of the homeomorphism to the full Jordan domains in question. The now-classical Circle Index Lemma says that…

We establish a framework for extending invariants of sutured manifolds to invariants of pairs of sutured manifolds who differ by attaching a basic slice along a torus boundary component. In the particular case of (bordered-)sutured Floer…

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…

The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a…

Following Goresky, Kottwitz and MacPherson, we compute the homology of truncated affine Springer fibers in the unramified case but under a purity assumption. We prove this assumption in the equivalued case. The truncation parameter is…