Related papers: Classification of $A_{\mathfrak{q}}(\lambda)$ modu…

We construct and compare three D-module models for the minimal representation of the conformal group of an even-dimensional quadratic space. Let $V$ be a quadratic space over a field $\kappa$ of characteristic $0$, let $C$ be the isotropic…

Let $\mathfrak{g}$ be a complex Kac-Moody algebra, with Cartan subalgebra $\mathfrak{h}$. Also fix a weight $\lambda\in\mathfrak{h}^*$. For $M(\lambda)\twoheadrightarrow V$ an arbitrary highest weight $\mathfrak{g}$-module, we provide a…

Let $G$ be a countable group. We introduce several equivalence relations on the set ${\rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $\lambda_{G/H}$ associated to $H\in {\rm Sub}(G)$ and compare…

Let $V$ be a vertex algebra of countable dimension, $G$ a subgroup of ${\rm Aut} V$ of finite order, $V^{G}$ the fixed point subalgebra of $V$ under the action of $G$, and ${\mathscr S}$ a finite $G$-stable set of inequivalent irreducible…

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 $U(\mathfrak{g},e_2)$,…

In this paper we consider non-abelian 1-cohomology for groups with coefficients in other groups. We prove versions of the `five lemma' arising from this situation. We go on to show that a connected unipotent algebraic group Q acted on…

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

For symplectic Lie algebras $\mathfrak{sp}(2n,\mathbb{C})$, denote by $\mathfrak{b}$ and $\mathfrak{n}$ its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of…

We study the $H_n(0)$-module $\mathbf{S}^\sigma_\alpha$ due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux and decomposed into cyclic submodules. First, we…

Let $(V,q)$ be a non-degenerate $n$-dimensional quadratic space over the rationals of real signature $(r,s)$. For every integer $1\leq k \leq \min\{r,n-2\}$ we construct classes in the cohomology of arithmetic subgroups of $\mathrm{O}(V)$…

Let $H_{\mathbf{k}}$ be a symplectic reflection algebra corresponding to a cyclic subgroup $\Gamma \subseteq SL_2 \C$ of order $n$ and $U_{\mathbf{k}} = eH_{\mathbf{k}} e$ the spherical subalgebra of $H_{\mathbf{k}}$. We show that for…

To any closed subvariety $Y$ of a complex abelian variety one can attach a reductive algebraic group $G$ which is determined by the decomposition of the convolution powers of $Y$ via a certain Tannakian formalism. For a theta divisor $Y$ on…

Let $\mathfrak{g}$ be a Lie algebra over an algebraically closed field $\Bbbk$ of characteristic zero. Define the universal grading group $\mathcal{C}(\mathfrak{g})$ as having one generator $g_{\rho}$ for each irreducible…

For any rank-one Riemannian symmetric space S of non-compact type and any discrete, cofinite, non-cocompact, torsion-free group $\Gamma$ of orientation-preserving Riemannian isometries on S, we develop a cohomological interpretation for the…

Let $A$ be the ring of elements in an algebraic function field $K$ over a finite field $F_q$ which are integral outside a fixed place $\infty$. In an earlier paper we have shown that the Drinfeld modular group $G=GL_2(A)$ has automorphisms…

Let $G_{\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\mathbb{R}}$ and assume that ${\rm rank}(G_\mathbb{R})={\rm rank}(K_\mathbb{R})$. For any representation $X$ of Gelfand-Kirillov dimension $\frac{1}{2}…

Let $G$ be a $p$-adic group that splits over an unramified extension. We decompose $Rep_{\Lambda}^{0}(G)$, the abelian category of smooth level $0$ representations of $G$ with coefficients in $\Lambda=\overline{\mathbb{Q}}_{\ell}$ or…

The paper explores the indecomposable submodule structures of quantum divided power algebra $\mathcal{A}_q(n)$ defined in \cite{HU} and its truncated objects $\mathcal{A}_q(n, \bold m)$. An "intertwinedly-lifting" method is established to…

Here we show that, given a finite homological system $({\cal P},\leq,\{\Delta_u\}_{u\in {\cal P}})$ for a finite-dimensional algebra $\Lambda$ over an algebraically closed field, the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules…

Let $G$ be a simple, simply-connected algebraic group defined over $\mathbb{F}_p$. Given a power $q = p^r$ of $p$, let $G(\mathbb{F}_q) \subset G$ be the subgroup of $\mathbb{F}_q$-rational points. Let $L(\lambda)$ be the simple rational…