Related papers: Blocks of the category $\mathcal{O}^\mathfrak{p}$ …

We prove that the center of a regular block of parabolic category O for the general linear Lie algebra is isomorphic to the cohomology algebra of a corresponding Springer fiber. This was conjectured by Khovanov. We also find presentations…

Using tools from the geometry of Einstein solvmanifolds, we give a geometric argument that a semi-simple Lie algebra (of non-compact type) is completely determined by its Iwasawa subalgebra. Furthermore, we produce an algebraic procedure…

In this paper we give algebraic models for rational G-spectra for a compact Lie group G when the geometric isotropy is restricted to lie in a 1-dimensional block of conjugacy classes. This includes all blocks of all groups of dimension 1,…

We present two novel proofs of the known classification of connected affine algebraic supergroups $G$ such that $\operatorname{Rep}G$ is semisimple. The proofs are geometrically motivated, although both rely on an algebraic lemma that…

We define a quantum version of Hamiltonian reduction by stages, producing a construction in type A for a quantum Hamiltonian reduction from the W-algebra $U(\mathfrak{g},e_1)$ to an algebra conjecturally isomorphic to $U(\mathfrak{g},e_2)$,…

Inspired by recent activities on Whittaker modules over various (Lie) algebras we describe some general framework for the study of Lie algebra modules locally finite over a subalgebra. As a special case we obtain a very general setup for…

The goal of this paper is to compute the supports of simple modules in the categories $\mathcal{O}$ for the rational Cherednik algebras associated to groups $G(\ell,1,n)$. For this we compute some combinatorial maps on the set of simples:…

We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…

We give a complete classification of the class of Lie algebras of simply connected real Lie groups whose nontrivial coadjoint orbits are of codimension 1. Such a Lie group belongs to a well-known class, called the class of MD-groups. The…

This paper classifies the blocks of the truncated $q$-Schur algebras of type $A$ which have as weight poset an arbitrary cosaturated set of partitions.

We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of…

This paper is a sequel to arXiv:2307.13358 and arXiv:2308.16090. A construction associating a semialgebra with an algebra, subalgebra, and a coalgebra dual to the subalgebra played a central role in the author's book arXiv:0708.3398. In…

We study monoidal categorifications of certain monoidal subcategories $\mathcal{C}_J$ of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures coincide and arise from the category of finite-dimensional…

W-algebras are a class of non-commutative algebras related to the classical universal enveloping algebras. They can be defined as a subquotient of U(g) related to a choice of nilpotent element e and compatible nilpotent subalgebra m. The…

This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…

We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…

We study {\em disemisimple} Lie algebras, i.e., Lie algebras which can be written as a vector space sum of two semisimple subalgebras. We show that a Lie algebra $\mathfrak{g}$ is disemisimple if and only if its solvable radical coincides…

To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with…

We characterize the solvable Lie groups of the form ${\mathbb R}^m\rtimes {\mathbb R}$, whose $C^*$-algebras are quasidiagonal. Using this result, we determine the connected simply connected solvable Lie groups of type~I whose…

Given a hyperplane arrangement in a complex vector space of dimension n, there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension k*n. Topological invariants of the complement of this…