相关论文: Euler Characteristic of Springer fibers

We give explicit formulas on total Springer representations for classical types. We also describe the characters of restrictions of such representations to a maximal parabolic subgroup isomorphic to a symmetric group. As a result, we give…

For a Weyl group $W$ of classical type, we present a formula to calculate the restriction of (graded) Springer representations of $W$ to a maximal parabolic subgroup $W'$ where the types of $W$ and $W'$ are in the same series. As a result,…

Let $W$ be the Weyl group of type $BC_n$. We first provide restriction formulas of the total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case to the maximal parabolic subgroup of $W$ which is…

In this paper we give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne-Lusztig variety if we replace Frobenius morphism with conjugation by an element for $GL_n$. The main theorem states that it only…

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid…

Let G be a simple reductive group over the complex numbers. Let W be the Weyl group of G. We propose a description of the Springer representations of W associated to various unipotent classes of G by a purely algebraic method involving the…

We derive a general formula for the Euler characteristic of a fibration of projective hypersurfaces in terms of invariants of an arbitrary base variety. When the general fiber is an elliptic curve, such formulas have appeared in the physics…

We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials and for ensembles related to nonorientable…

We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi…

This manuscript contains tables giving the multiplicities with which irreducible characters of exceptional Weyl groups appear in characters induced from certain reflection subgroups containing maximal parabolic subgroups.

We compute Euler characteristics of p-subgroup categories of finite groups

We establish a relation between the known parametrization of a family of irreducible representations of a Weyl group and Springer's correspondence. We outline a parametrization of unipotent character sheaves on a connected reductive group…

We extend the Siu--Beauville theorem to a certain class of compact Kaehler--Weyl manifolds, proving that they fiber holomorphically over hyperbolic Riemannian surfaces whenever they satisfy the necessary topological hypotheses. As…

We give a common framework for the classification of projective spin irreducible representations of a Weyl group, modeled after the Springer correspondence for ordinary representations.

In this paper we discuss some of Springer's work on unipotent elements in a reductive groups and on representations of Weyl groups. Among the topics considered are Springer's bijection from the unipotent variety to the nilpotent variety,…

For maximal compact subgroups of the metaplectic group, the minimal types in the Schr\"odinger model of the Weil representation are calculated explicitly. Although these types are known in the case of odd residual characteristic, this…

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set…

We extend a result of Yun on minimal reduction types to the parahoric case. This implies a uniqueness property for 2-special representations appearing in the cohomology of certain affine Springer fibers. Using this, we settle a conjecture…

For an $n$-fold geometrically cyclic branched covering $Y$ of a smooth, projective scheme $X$ branched at a smooth closed subscheme $Z\subset X$ with $n \in k^\times$, we compute the quadratic Euler characteristic of $Y$ in terms of certain…

We propose a definition of an Euler characteristic for unbounded chain complexes by taking the (usual) Euler characteristics of successively longer parts of the complex, weighted inversely proportional to the length, and passing to the…