相关论文: Representations and identities of plactic-like mon…

We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…

A fully invarient congruence relations on the free algebra on a given type induces a variety of the given type. In contrast, a congruence relation of the free algebra provides algebra of that type. This algebra is given by a so-called…

Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This…

We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with $\mathfrak g={\sf Lie}(G)$ such that the symmetric invariants of the semi-direct product $\mathfrak g\ltimes V$, where $V$ is an…

There exist several theorems which state that when a matroid is representable over distinct fields F_1,...,F_k, it is also representable over other fields. We prove a theorem, the Lift Theorem, that implies many of these results. First,…

We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutations, pairs of twin binary trees,…

We give a general multiplication-convolution identity for the multivariate and bivariate rank generating polynomial of a matroid. The bivariate rank generating polynomial is transformable to and from the Tutte polynomial by simple algebraic…

In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strata are locally modelled by $\R^k$ modulo the action of a…

We completely determine all varieties of monoids on whose free objects all fully invariant congruences or all fully invariant congruences contained in the least semilattice congruence permute. Along the way, we find several new monoid…

This is a foundational paper in tropical linear algebra, which is linear algebra over the min-plus semiring. We introduce and compare three natural definitions of the rank of a matrix, called the Barvinok rank, the Kapranov rank and the…

Lawrence-Krammer representations (LK-representations for short) are linear representations of Artin-Tits groups of small type, which are of importance since they are known to be faithful when the type is spherical, or more generally when…

We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable…

Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety $\mathbb E^1$ whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely…

We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to infinity in certain directions. Such an arrangement defines a decomposition of Euclidean space where a cell is determined by its `type' data,…

We obtain presentations for the Brauer monoid, the partial analogue of the Brauer monoid, and for the greatest factorizable inverse submonoid of the dual symmetric inverse monoid. In all three cases we apply the same approach, based on the…

We investigate toric varieties defined by arrangements of hyperplanes and call them strongly symmetric. The smoothness of such a toric variety translates to the fact that the arrangement is crystallographic. As a result, we obtain a…

The main goal of this note is to provide evidence that the first rational homology of the Johnson subgroup $K_{g,1}$ of the mapping class group of a genus g surface with one marked point is finite-dimensional. Building on work of…

Graph monoids arise naturally in the study of non-stable K-theory of graph C*-algebras and Leavitt path algebras. They play also an important role in the current approaches to the realization problem for von Neumann regular rings. In this…

A connection relating Tamari lattices on symmetric groups regarded as lattices under the weak Bruhat order to the positive monoid P of Thompson group F is presented. Tamari congruence classes correspond to classes of equivalent elements in…

Consider the quotient $G/B$ of a simple matrix Lie group $G$ by a subgroup $B$ isomorphic to a direct product of some of $S^1$s and $S^3$s such that its adjoint representation can be extended over $G$. Then it naturally inherits a stable…