Related papers: Relating Edelman-Greene insertion to the Little ma…
Fix an integral semisimple element $\lambda$ in the Lie algebra $\mathfrak{g}$ of a complex reductive algebraic group $G$. Let $L$ denote the centralizer of $\lambda$ in $G$ and let $\mathfrak{g}(-1)$ denote the $-1$ eigenspace of…
Bauer and Itzykson showed that associated to each labeled map embedded on an oriented Riemann surface there was a group generated by a pair of permutations. From this result an algorithm may be constructed for enumerating labeled maps, and…
The Robinson-Schensted-Knuth (RSK) algorithm maps an integer matrix to a pair of semi-standard Young tableaux (SSYTs) whose underlying shape has the same integer partition. We study the set of matrices associated with a given partition…
Given a probability measure $\mu$ over ${\mathbb R}^n$, it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan…
In this paper, we describe an algorithm for computing the left, right, or 2-sided congruences of a finitely presented semigroup or monoid with finitely many classes, and an alternative algorithm when the finitely presented semigroup or…
Through dualities on representations on tensor powers and symmetric powers respectively, the partition algebra and multiset partition algebra have been used to study long-standing questions in the representation theory of the symmetric…
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
We study random typical minimal factorizations of the $n$-cycle, which are factorizations of $(1, \ldots,n)$ as a product of $n-1$ transpositions, chosen uniformly at random. Our main result is, roughly speaking, a local convergence theorem…
Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the…
We continue our investigation into the insertion-elimination Lie algebra of Feynman graphs in the ladder case, emphasizing the structure of this Lie algebra relevant for future applications in the study of Dyson-Schwinger equations. We work…
R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets of rim-hooks of the same partition shape. It is known that…
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…
Using a generalization of the Schensted insertion algorithm to rc-graphs, we provide a Littlewood-Richardson rule for multiplying certain Schubert polynomials by Schur polynomials.
Results of Morse and Schilling show that the set of increasing factorizations of reduced words for a permutation is naturally a crystal for the general linear Lie algebra. Hiroshima has recently constructed two superalgebra analogues of…
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…
This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…