Related papers: On regularity in codimension one of irreducible co…

Let A be a self-injective algebra over an algebraically closed field k. We show that if an A-module M of complexity one has an open orbit in the variety of d-dimensional A-modules, then M is periodic. As a corollary we see that any simple…

Let k be an algebraically closed field and A be a finite-dimensional associative basic k-algebra of the form A=kQ/I where Q is a quiver without oriented cycles or double arrows and I is an admissible ideal of kQ. We consider roots of the…

Let $\Lambda$ be a local truncated path algebra over an algebraically closed field $K$, i.e., $\Lambda$ is a quotient of a path algebra $KQ$ by the paths of length $L+1$, where $Q$ is the quiver with a single vertex and a finite number of…

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

Let $k$ be an algebraically closed field of characteristic 2. We compute the vertices of all indecomposable $kD_8$-modules for the dihedral group $D_8$ of order 8. We also give a conjectural formula of the induced module of a string module…

We consider a bipartite distance-regular graph $G$ with diameter at least 4 and valency at least 3. Fix a vertex of $G$ and let $T$ denote the corresponding subconstituent algebra. We give a detailed description of a certain type of…

We prove the basic properties of determinantal semi-invariants for presentation spaces over any finite dimensional hereditary algebra over any field. These include the virtual generic decomposition theorem, stability theorem and the…

Fix a finite field $\mathbb{F}$. Let $\mathrm{VI}$ be a skeleton of the category of finite dimensional $\mathbb{F}$-vector spaces and injective $\mathbb{F}$-linear maps. We study $\mathrm{VI}^m$-modules over a noetherian commutative ring in…

We prove some basic results on the dimension theory of algebraic stacks, and on the multiplicities of their irreducible components, for which we do not know a reference.

Let M be a complex of D-modules with bounded holonomic cohomology on a complex manifold. In this note, we prove that if the derived tensor product of M with itself is regular, then M is regular.

A conjecture of De Concini Kac and Procesi provides a bound on the minimal possible dimension of an irreducible module for quantized enveloping algebras at an odd root of unity. We pose the problem of the existence of modules whose…

Let $k$ be an algebraically closed field. Fix integers $n$ and $b$ with $n\geq 3$ and $1\leq b\leq n-1.$ Let $T^d_k$ be the moduli space of hypersurfaces $[F]$ in $\mathbb{P}^n_k$ of degree $l$ whose singular locus contains a subscheme of…

We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $1$ or $3$. We prove that the variety is the union of Zariski closures of the orbits of $11$ and $21$ rigid superalgebras,…

The invariant eigendistributions on a reductive Lie algebra are solutions of a holonomic D-module which has been proved to be regular by Kashiwara-Hotta. We solve here a conjecture of Sekiguchi saying that in the more general case of…

Let $\Aa_t$ be the directed quiver of type $\Aa$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the…

Let (G,V) be a regular prehomogeneous vector space (abbreviated to PV), where G is a connected reductive algebraic group over C. If $V= \oplus_{i=0}^{n}V_{i}$ is a decomposition of V into irreducible representations, then, in general, the…

A subvariety of a quasi-projective complex variety $X$ is called ``universally irreducible'' if its preimage inside the universal cover of $X$ is irreducible. In this paper we investigate sufficient conditions for universal irreducibility.…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…

We establish the essential normality of a large new class of homogeneous submodules of the finite rank d-shift Hilbert module. The main idea is a notion of essential decomposability that determines when an arbitrary submodule can be…

Let $A$ be a finite dimensional associative $\mathbb{K}$-algebra over an algebraically closed field $\mathbb{K}$ of characteristic zero. To $A$, we can associate its basic form that is given by a quiver $Q = (Q_0, Q_1)$ with an admissible…