Related papers: Parabolic induction for Springer fibres

In this note we construct a "restriction" map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to parabolic induction and deduce that…

Consider a complex classical semi-simple Lie group along with the set of its nilpotent coadjoint orbits. When the group is of type A, the set of orbital varieties contained in a given nilpotent orbit is described a set of standard Young…

The orbital varieties are the irreducible components of the intersection between a nilpotent orbit and a Borel subalgebra of the Lie algebra of a reductive group. There is a geometric correspondence between orbital varieties and irreducible…

For $G=GL(n,\mathbb{C})$ and a parabolic subgroup $P=LN$ with a two-block Levi subgroup $L=GL(n_1)\times GL(n_2)$, the space $G\cdot (\mathcal{\mathcal{O}}+\mathfrak{n})$, where $\mathcal{O}$ is a nilpotent orbit of $\mathfrak{l}$, is a…

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

Let $G$ be a simple algebraic group over the complex field $\mathbb C$, $P$ a parabolic subgroup containing $B$ its Borel subgroup, $P'$ its derived group and $\mathfrak m$ the Lie algebra of its nilradical. The nilfibre $\mathscr N$ for…

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…

Let $G$ be a compact connected semisimple Lie group with Lie algebra $\mathfrak{g}$. Let $\mathcal{O}\subset\mathfrak{g}^*$ be a coadjoint orbit. The action of $G$ on $\mathcal{O}$ induces a morphism $\rho:G\to \mathrm{Homeo}(\mathcal{O})$.…

Let $B{ aut}_1X$ be the Dold-Lashof classifying space of orientable fibrations with fiber $X$. For a rationally weakly trivial map $f:X\to Y$, our strictly induced map $a_f: (Baut_1X)_0\to (Baut_1Y)_0$ induces a natural map from a…

Let $G$ be a connected reductive group over an algebraically closed field $k$, and let $Fl$ be the affine flag variety of $G$. For every regular semisimple element $\gamma$ of $G(k((t)))$, the affine Springer fiber $Fl_{\gamma}$ can be…

Let $G$ be a connected, reductive algebraic group over an algebraically closed field $k$ of prime characteristic $p$ and $\mathfrak{g}=Lie(G)$. In this paper, we study representations of $\mathfrak{g}$ with a $p$-character $\chi$ of…

We give a self-contained account of a construction due to Rossmann which lifts Springer's action of a Weyl group on the cohomology of a Springer fiber to an action on its homotopy type. We use this construction to produce a generalization…

Let G be a connected reductive algebraic group over an algebraically closed field k. We consider the strata in G defined by Lusztig as fibers of a map given in terms truncated induction of Springer representations. We extend to arbitrary…

Given a reductive group $G$, we give a description of the abelian category of $G$-equivariant $D$-modules on $\mathfrak{g}=\mathrm{Lie}(G)$, which specializes to Lusztig's generalized Springer correspondence upon restriction to the…

Ariki and Ginzburg, after the previous work of Zelevinsky on orbital varieties, proved that multiplicities in a total parabolically induced representations are given by the value at q=1 of Kazhdan-Lusztig Polynomials associated to the…

Let $G$ be a real semisimple Lie group with finite center and let $\mathfrak g=\mathfrak k \oplus \mathfrak p$ be a Cartan decomposition of its Lie algebra. Let $K$ be a maximal compact subgroup of $G$ with Lie algebra $\mathfrak k$ and let…

In this article, we present two novel approaches to constructing weighted orbital integrals of an inner form of a general linear group. Our method utilizes generalized Lustig-Spaltenstein induction. Furthermore, we will prove that a…

We extend the notion of induced conjugacy classes in reductive groups, introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary classes. We study properties of equivariant fibrations of prehomogeneous affine spaces,…

We study a certain cycle map defined on finite dimensional modules for the W-algebra with regular integral central character. Via comparison with the theory in postive characteristic, we show that this map injects into the top Borel-Moore…

The flag variety of a complex reductive linear algebraic group G is by definition the quotient G/B by a Borel subgroup. It can be regarded as the set of Borel subalgebras of Lie(G). Given a nilpotent element e in Lie(G), one calls Springer…