Related papers: An exotic Springer correspondence for symplectic g…

Let G = Sp (2n) be the symplectic group over Z. We present a certain kind of deformation of the nilpotent cone of G with G-action. This enables us to make direct links between the Springer correspondence of sp_{2n} over C, that over…

Let G be a complex symplectic group. We introduce a G x (C ^x) ^{l + 1}-variety N_{l}, which we call the l-exotic nilpotent cone. Then, we realize the Hecke algebra H of type C_n ^(1) with three parameters via equivariant algebraic K-theory…

Let V be an 2n-dimensional vector space over an algebraically closed field of odd characteristic. Let G = GL(V), and H = Sp(V) the symplectic group contained in G. For a positive integer r > 1, we conisder the variety X = G/H \times…

Let $G$ be a simply connected algebraic group of type $B,C$ or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we…

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over $\tF_{2^n}$. Let $G$ be an adjoint algebraic group of type $B,C$ or $D$ defined over an algebraically closed field…

Let V be a 2n dimensional vector space over an algebraically closed field of odd characteristic. Let G = GL(V) and H = Sp_{2n} be the symplectic group contained in G. We call X = G/H \times V the exotic symmetric space, since its…

Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie algebras in…

This paper is a survey on the topics concerning the Springer correspondence related to the varieties such as the enhanced variety or the exotic symmetric space. We explain in the case of exotic symmetric space of higher level, the complex…

We investigate the structure of the `exotic nilcone' of $F_4$ which is defined by exploiting certain characteristic two phenomena. We show that there are finitely many orbits on this nilcone and construct an associated Springer…

Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to an equivalence between the triangulated category generated by the Springer…

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…

Kato's exotic nilpotent cone was introduced as a substitute for the ordinary nilpotent cone of type C with cleaner properties. The geometric Robinson-Schensted correspondence is obtained by parametrizing the irreducible components of the…

Kato introduced the exotic nilpotent cone to be a substitute for the ordinary nilpotent cone of type C with cleaner properties. Here we describe the irreducible components of exotic Springer fibres (the fibres of the resolution of the…

We complete the construction of the modular generalized Springer correspondence for an arbitrary connected reductive group, with a uniform proof of the disjointness of induction series that avoids the case-by-case arguments for classical…

The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra. In this article, we consider a modular version of the theory, and show that…

We introduce the notion of a conical symplectic variety, and show that any symplectic resolution of such a variety is isomorphic to the Springer resolution of a nilpotent orbit in a semisimple Lie algebra, composed with a linear projection.

This short note is a supplement to the previous article with the same title. Here we treat a conical symplectic variety obtained as a finite covering of a (not necessarily normal) nilpotent orbit closure of a complex semisimple Lie algebra.

Let $G=Sp_{2n}(\mathbb{C})$, and $\mathfrak{N}$ be Kato's exotic nilpotent cone. Following techniques used by Bezrukavnikov in [5] to establish a bijection between $\Lambda^+$, the dominant weights for a simple algebraic group $H$, and…

The global nilpotent cone N is a singular stack associated to the choice of an algebraic group G, a smooth projective curve X, and a line bundle L on X, which is of fundamental importance to the Geometric Langlands Program, and which is of…

Let $G = GL(V)$ for an N-dimensional vector space $V$ over an algebraically closed field k, and $G^{\theta}$ the fixed point subgroup of $G$ under an involution $\theta$ on $G$. In the case where $G^{\theta} = O(V)$, the generalized…