Related papers: Springer correspndence for complex reflection grou…

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…

This is a survey article on the Springer correspondence for symmetric spaces. We discuss various generalization of the theory of the Springer correspondence for reductive groups to symmetric spaces and exotic symmetric spaces associated to…

The Lusztig-Shoji algorithm is generalized to a complex reflection group $W$ and give us a version of the Springer correspondence of $W$. We show that the combinatorics of generalized Springer correspondences of dihedral groups of order…

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…

In this paper, we obtain an explicit formula for the theta correspondence of unipotent principal-series representations between an even orthogonal and a symplectic group or between general linear groups over a finite field. The formula is…

Let $G = GL_N$ over an algebraically closed field of odd characteristic, and $\theta$ an involutive automorphism on $G$ such that $H = (G^{\theta})^0$ is isomorphic to $SO_N$. Then $G^{\iota\theta} = \{ g \in G \mid \theta(g) = g^{-1} \}$…

Recent work by a number of people has shown that complex reflection groups give rise to many representation-theoretic structures (e.g., generic degrees and families of characters), as though they were Weyl groups of algebraic groups.…

In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail…

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…

This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372, arXiv:0806.0867] by the authors and in the paper [Algebr. Represent. Theory 13 (2010),…

We study the construction of a modular generalized Springer correspondence for a possibly disconnected complex reductive algebraic group.

We define a generalized Springer correspondence for the group GL(n) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse…

We give a combinatorial description of the Springer correspondence for classical Lie algebras $\mathfrak{g}$ of type $B,C$ or $D$ and their duals $\mathfrak{g}^*$ in characteristic 2. The combinatorics used here is of the same kind as those…

In \cite{CVX3}, we have established a Springer theory for the symmetric pair $(\operatorname{SL}(N),\operatorname{SO}(N))$. In this setting we obtain representations of (the Tits extension) of the braid group rather than just Weyl group…

In this paper we establish Springer correspondence for the symmetric pair $(\mathrm{SL}(N),\mathrm{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaves construction due to Grinberg. As applications, we…

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.

Hierarchies of evolution equations of pseudo-spherical type are introduced, generalizing the notion of a single equation describing pseudo-spherical surfaces due to S.S. Chern and K. Tenenblat, and providing a connection between…

We describe the Springer correspondence explicitly for exceptional Lie algebras of type $G_2$ and $F_4$ and their duals in bad characteristics, i.e. in characteristics 2 and 3.

We close a gap in the explicit determination of the generalized Springer correspondence for a connected reductive group in good characteristic.

We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group $\mathrm{Mp}_2$, to the metaplectic group $\mathrm{Mp}_{2n}$ of higher rank. To establish…