Related papers: A hierarchy of parametrizing varieties for represe…

We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a key example in non-semisimple higher representation theory.…

In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F.…

This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…

Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…

We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…

A numerical description of an algebraic subvariety of projective space is given by a general linear section, called a witness set. For a subvariety of a product of projective spaces (a multiprojective variety), the corresponding numerical…

In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties…

Schubert varieties of hyperplane arrangements, also known as matroid Schubert varieties, play an essential role in the proof of the Dowling-Wilson conjecture and in Kazhdan-Lusztig theory for matroids. We study these varieties as…

This thesis studies the representation theory and linear structures of $\mathcal{Q}$-manifolds and higher Lie algebroids. We introduce differential graded modules (or for short DG-modules) of $\mathcal{Q}$-manifolds and the equivalent…

Let $G$ be a finite group. In the first part of the paper we develop further the foundations of the youngly introduced glider representation theory. Glider representations encompass filtered modules over filtered rings and as such carry…

We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…

We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…

Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…

Let $X$ be a normal complex projective variety, $T\subseteq X$ a subvariety, $a\colon X\rightarrow A$ a morphism to an abelian variety such that $\rm{Pic}^0(A)$ injects into $\rm{Pic}^0(T)$ and let $L$ be a line bundle on $X$. Denote by…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

We introduce support varieties for rational representations of a linear algebraic group $G$ of exponential type over an algebraically closed field $k$ of characteristic $p > 0$. These varieties are closed subspaces of the space $V(G)$ of…

The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree $d$ in $n+1$ variables on an algebraically closed field, called $\Split_{d}(\PP n)$, with the Grassmannian of $n-1$…

This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…

We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave…

Let $G$ be a reductive algebraic group over a $p$-adic field or number field $K$, and let $V$ be a $K$-linear faithful representation of $G$. A lattice $\Lambda$ in the vector space $V$ defines a model $\hat{G}_{\Lambda}$ of $G$ over…