Related papers: Generalized Springer Theory for D-modules on a Red…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

A Lie algebra is said to be generalised reductive if it is a direct sum of a semisimple Lie algebra and a commutative radical. In this paper we extend the BGG category $\mathcal{O}$ over complex semisimple Lie algebras to the category…

Let G be a reductive connected p-adic group. With help of the Fourier inversion formula used in [Une formule de Plancherel pour l'algebre de Hecke d'un groupe reductif p-adique - V. Heiermann, Comm. Math. Helv. 76, 388-415, 2001] we give a…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

Let G be a reductive group over a non-archimedean local field and let S(G) be its Schwartz algebra. We compare Ext-groups of tempered G-representations in several module categories: smooth G-representations, algebraic S(G)-modules,…

We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the…

Let $F$ be an algebraically closed field and consider the Lie algebra ${\mathfrak g}=\langle x\rangle\ltimes {\mathfrak a}$, where $\mathrm{ad}\, x$ acts diagonalizably on the abelian Lie algebra ${\mathfrak a}$. Refer to a ${\mathfrak…

Let $A$ be a condensable algebra in a modular tensor category $\mathcal{C}$. We define an action of the fusion category $\mathcal{C}_A$ of $A$-modules in $\mathcal{C}$ on the morphism space $\mbox{Hom}_{\mathcal{C}}(x,A)$ for any $x$ in…

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…

The Springer resolution of the nilpotent cone of a semisimple Lie algebra has played an important role in representation theory. The nilpotent cone is equal to Spec R, where R is the ring of regular functions on the nilpotent cone. This…

The consistent systems of idempotents of Meyer and Solleveld allow to construct Serre subcategories of $Rep_R(G)$, the category of smooth representations of a $p$-adic group $G$ with coefficients in $R$. In particular, they were used to…

Let G be a general linear group over a p-adic field and let D^* be an anisotropic inner form of G. The Jacquet-Langlands correspondence between irreducible complex representations of D^* and discrete series of G does not behave well with…

Given the nilpotent cone of a complex reductive Lie algebra, we consider its equivariant constructible derived category of sheaves with coefficients in an arbitrary field. This category and its subcategory of perverse sheaves play an…

If G is a finite group and k is a field, there is a natural construction of a Hopf algebra over k associated to G, the Drinfel'd double D(G). We prove that if G is any finite real reflection group with Drinfel'd double D(G) over an…

We study D-modules and related invariants on the space of 2 x 2 x n hypermatrices for n >= 3, which has finitely many orbits under the action of G = GL_2 x GL_2 x GL_n. We describe the category of coherent G-equivariant D-modules as the…

We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra…

We continue the systematic study of left-invariant generalised Einstein metrics on Lie groups initiated in arXiv:2206.01157. Our approach is based on a new reformulation of the corresponding algebraic system. For a fixed Lie algebra…

We give a simple algebraic model for rational G-spectra over an exceptional subgroup, for any compact Lie group G. Moreover, all our Quillen equivalences are symmetric monoidal, so as a corollary we obtain a monoidal algebraic model for…

For a smooth complex algebraic curve $X$ and a reduced effective divisor $D$ on $X$, we introduce a notion of $D$-level structure on parahoric $\mathcal{G}_{\boldsymbol \theta}$-torsors over $X$, for any connected complex reductive Lie…