Related papers: Characteristic polynomials and finitely dimensiona…

We prove that the number of geometrically indecomposable representations of fixed dimension vector d of a canonical algebra C defined over a finite field Fq is given by a polynomial in q (depending on C and d). We prove a similar result for…

We present and study two families of polynomials with coefficients in the center of the universal enveloping algebra. These polynomials are analogues of a determinant and a characteristic polynomial of a certain non-commutative matrix,…

We define extended SL(2,R)/U(1) characters which include a sum over winding sectors. By embedding these characters into similarly extended characters of N=2 algebras, we show that they have nice modular transformation properties. We…

In this paper, we compute the E-polynomials of the $PGL(2,\mathbb{C})$-character varieties associated to surfaces of genus $g$ with one puncture, for any holonomy around it, and compare it with its Langlands dual case, $SL(2,\mathbb{C})$.…

For the Borromean link, we determine its irreducible ${\rm SL}(2,\mathbb{C})$-character variety, and find a formula for the twisted Alexander polynomial as a function on the character variety.

We describe the set of characteristic polynomials of abelian varieties of dimension 4 over finite fields.

For a field $E$ of characteristic different from $2$ and cohomological $2$-dimension one, quadratic forms over the rational function field $E(X)$ are studied. A characterisation in terms of polynomials in $E[X]$ is obtained for having that…

Let k be a field of characteristic not two or three, let $\mathfrak{g}$ be a finite-dimensional colour Lie algebra and let V be a finite-dimensional representation of $\mathfrak{g}$. In this article we give various ways of constructing a…

A basis for each finite-dimensional irreducible representation of the symplectic Lie algebra sp(2n) is constructed. The basis vectors are expressed in terms of the Mickelsson lowering operators. Explicit formulas for the matrix elements of…

We associate to a semisimple complex Lie algebra $\mathfrak{g}$ a sequence of polynomials $P_{\ell,\mathfrak{g}}(x)\in\mathbb{Q}[x]$ in $r$ variables, where $r$ is the rank of $\mathfrak{g}$ and $\ell=0,1,2,\ldots $. The polynomials…

In this paper we generalize the classical Groebner basis technique to prove the existence and present a method of computation of a dimension polynomial in two variables associated with a finitely generated D-module, that is, a finitely…

This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce…

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…

A survey of the theory of Kac polynomials for quivers and for curves. In particular, we describe the representation-theoretic meaning of Kac polynomials in terms of Hall algebras, and the geometric meaning of Kac polynomials in relation to…

A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of…

The category of representations with a strongly typical central character of a basic classical Lie superalgebra is proven to be equivalent to the category of representations of its even part corresponding to an appropriate central…

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…

We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.

The typical definition of the characteristic polynomial seems totally ad hoc to me. This note gives a canonical construction of the characteristic polynomial as the minimal polynomial of a "generic" matrix. This approach works not just for…

Let $\Bbbk$ be an algebraically closed field of characteristic $2$ and let $\mathfrak{fsl}(2)$ be the unique, up to isomorphism, $3$-dimensional simple Lie algebra over $\Bbbk$. Denote by $\mathfrak{m}$ the minimal $2$-envelope of…