Related papers: Ideals, representations and a symmetrised Bernoull…

We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.

We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and regular powers, and on the combinatorics of the symbolic…

We study embeddings of symmetric groups to the space Cremona group.

We study ideals generated by $n+1$ powers of general linear forms in $R= k[x_1,\dots,x_n]$. By generalizing the ideas in a recent paper of Diethorn et al., we determine the Betti numbers of such ideals when at least one generator is a…

Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case.…

We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

We develop Fenchel-Nielsen coordinates for representations of surface groups into Sp(2n,R) with maximal Toledo invariant. Analogous to classical Fenchel-Nielsen coordinates on the Teichm\"uller space they consist of a parametrization of…

We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…

We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.

We completely solve the equivalence problem for Euler-Bernoulli equation using Lie symmetry analysis. We show that the quotient of the symmetry Lie algebra of the Bernoulli equation by the infinite-dimensional Lie algebra spanned by…

We introduce truncation ideals of a $\Bbbk$-linear unitary symmetric operad and use them to study ideal structure, growth property and to classify operads of low Gelfand-Kirillov dimension.

We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…

Given a monoidal triangulated category $T$ with noetherian spectrum, we show that there is an order preserving bijection between the collection of all Thomason subsets of the non-commutative spectrum $\mathrm{Spc}(T)$ and the collection of…

We consider the polynomial ring in finitely many variables over an algebraically closed field of positive characteristic, and initiate the systematic study of ideals preserved by the action of the general linear group by changes of…

This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…

The problem of finding an appropriate geometrical/physical index for measuring a degree of inhomogeneity for a given space-time manifold is posed. Interrelations with the problem of understanding the gravitational/informational entropy are…

In the monograph arXiv:2108.03453, we define the notion of a unipotent representation of a complex reductive group. The representations we define include, as a proper subset, all special unipotent representations in the sense of…

The tempered spectrum of the similitude groups of non-degenerate symplectic, hermitian, or split orthogonal forms defined over $p$\snug-adic groups of characteristic zero is studied. The components of representations induced from discrete…