Related papers: Modules and Structures of Planar Upper Triangular …

In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and…

This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…

Let k be a field and A the n-Kronecker algebra, this is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is well-known that the dimension vectors of the indecomposable…

For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are…

Let $\mathbb K$ be an algebraically closed field of characteristic zero, $\mathbb K[X]$ the polynomial ring in $n$ variables. The vector space $T_n = \mathbb K[X]$ is a $\mathbb K[X]$-module with the action $x_i \cdot v = v_{x_i}'$ for $v…

Let $\mathfrak{M}_n$ be the multiplicative monoid of $n \times n$ matrices over a finite field. The monoid algebra $\mathbf{C}[\mathfrak{M}_n]$ has been studied for several decades. One of the important early results is Kov\'acs' theorem…

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions…

Fix any algebraic extension $\mathbb K$ of the field $\mathbb Q$ of rationals. In this article we study exponential sets $V\subset \mathbb R^n$. Such sets are described by the vanishing of so called exponential polynomials, i.e.,…

Let $H$ and $K$ be the bosonizations of the Jordan and super Jordan plane by the group algebra of a cyclic group; the algebra $K$ projects onto an algebra $L$ that can be thought of as the quantum Borel of $\mathfrak{sl}(2)$ at $-1$. The…

Let $G$ be a rank $n$ additive subgroup of $\bC$ and $\Vir[G]$ the corresponding Virasoro algebra of rank $n$. In the present paper, irreducible weight modules with finite dimensional weight spaces over $\Vir[G]$ are completely determined.…

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional…

Given a ring of ternions $R$, i. e., a ring isomorphic to that of upper triangular $2\times 2$ matrices with entries from an arbitrary commutative field $F$, a complete classification is performed of the vectors from the free left…

In this paper we compute the generating function of modular, $k$-noncrossing diagrams. A $k$-noncrossing diagram is called modular if it does not contains any isolated arcs and any arc has length at least four. Modular diagrams represent…

In this paper it is proved that an irreducible weight module with finite-dimensional weight spaces over the Schr\"{o}dinger-Virasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable…

A partition of the set of unary pp formulas into four regions is presented, which has a bearing on various structural properties of modules. The machinery developed allows for applications to IF, weakly coherent, nonsingular, and reduced…

A \textbf{single change covering design} is a $v$-set $X$ and an ordered list $\cL$ of $b$ blocks of size $k$ where every $t$-set must occur in at least one block. Each pair of consecutive blocks differs by exactly one element. A single…

We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a…

A class of indecomposable representations of U_q(sl_n) is considered for q an even root of unity (q^h = -1) exhibiting a similar structure as (height h) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field…

We present a method for obtaining congruences modulo powers of 3 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Motzkin numbers, Riordan numbers, Schr\"oder numbers,…

We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings…