Related papers: On the relation between pseudocharacters and Chene…

We prove an identity relating the permanent of a rank $2$ matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the…

An invertible matrix is called a Perron similarity if it diagonalizes an irreducible, nonnegative matrix. Each Perron similarity gives a nontrivial polyhedral cone, called the spectracone, and polytope, called the spectratope, of realizable…

Let $A$ be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Su\'arez result on the connection between reducibility in $A$ and…

We consider the following question: When are rings of differential operators coherent? If $A$ is a finitely generated smooth domain over a field $k$ of characteristic $0$, then the ring $D$ of differential operators on $A$ is a Noetherian…

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…

We give new definitions for the determinant over commutative ring $K$, noncommutative ring $\mathbf{K}$, noncommutative ring $\mathcal{K}$ with associative powers, over noncommutative nonassociative ring $\mathfrak{K}$, and study their…

This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that is the representation of a multivariate polynomial P by a symmetric matrix M such that P=det(M), and where each entry of M is either a constant or a…

We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged…

For an $n \times n$ nonnegative matrix $P$, an isomorphism is obtained between the lattice of initial subsets (of ${1,...,n}$) for $P$ and the lattice of $P$-invariant faces of the nonnegative orthant $\IR^{n}_{+}$. Motivated by this…

The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular…

We introduce the notion of relative pseudocoefficient for relative discrete series of real spherical homogeneous spaces of reductive groups. We prove that such relative pseudocoefficient does not exist for semisimple symmetric spaces of…

Let $d\geq 3$ be a fixed integer and $A$ be the adjacency matrix of a random $d$-regular directed or undirected graph on $n$ vertices. We show there exist constants $\mathfrak d>0$, \begin{align*} {\mathbb P}(\text{$A$ is singular in…

Let $A$ be an integral $k$-algebra of finite type over an algebraically closed field $k$ of characteristic $p>0$. Given a collection ${\cal{D}}$ of $k$-derivations on $A$, that we interpret as algebraic vector fields on $X=Spec(A)$, we…

We prove a dynamical Shafarevich theorem on the finiteness of the set of isomorphism classes of rational maps with fixed degeneracies. More precisely, fix an integer d at least 2 and let K be either a number field or the function field of a…

Let $R$ be an associative ring with a nonzero ideal $I$ and a semiprime ideal $T$ such that $T\subsetneq I.$ Let $K$ be a nonempty subset of $R$ and $d:R\to R$ be a derivation of $R$, if $[d(x),x]\in T$ for all $x\in K,$ then $d$ is said to…

Let $A$ be a unital $C^*$-algebra and let $U_0(A)$ be the group of unitaries of $A$ which are path connected to the identity. Denote by $CU(A)$ the closure of the commutator subgroup of $U_0(A).$ Let $i_A^{(1, n)}\colon…

A definition of $d$--dimensional $n$--Meixner random vectors is given first. This definition involves the commutators of their semi--quantum operators. After that we will focus on the $1$-Meixner random vectors, and derive a system of $d$…

We diagonalize the Hilbert space of some subclass of the quasifinite module of the \Winf algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of…

This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of $p$-adic symplectic and special orthogonal groups, near the identity element. We declare two…

Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of…