Related papers: Mixed Dimer Configuration Model in Type $D$ Cluste…
Motivated by a recent conjecture by Hernandez and Leclerc [arXiv:0903.1452], we embed a Fomin-Zelevinsky cluster algebra [arXiv:math/0104151] into the Grothendieck ring R of the category of representations of quantum loop algebras U_q(Lg)…
The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by…
In this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type $D_n$, inspired by Mukhin and Young's combinatorial path models of representations of the quantum affine algebras of types $A_n$…
In this paper, several conjectures proposed in [2] are studied, involving the equivalence and duality of polycyclic codes associated with trinomials. According to the results, we give methods to construct isodual and self-dual polycyclic…
F-polynomials and g-vectors were defined by Fomin and Zelevinsky to give a formula which expresses cluster variables in a cluster algebra in terms of the initial cluster data. A quantum cluster algebra is a certain noncommutative…
We construct a cofibrantly generated model structure on the category of differential non-negatively graded quasi-coherent commutative $D_X$-algebras, where $D_X$ is the sheaf of differential operators of a smooth afine algebraic variety X.…
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U be a cluster algebra of type A_n. We associate to each cluster C of U an abelian category Cat_C such that the indecomposable…
This is the second in a series of two papers developing a moduli-theoretic framework for differential ideal sheaves associated with formally integrable, involutive systems of algebraic partial differential equations (PDEs). Building on…
We study the classification of $\mathbb{Z}$-DGAs with polynomial homology $\mathbb{F}_p[x]$ with $\lvert x \rvert >0$, motivated by computations in algebraic $K$-theory. This classification problem was left open in work of Dwyer, Greenlees,…
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend…
Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from…
We give an overview of recent developments in the theory of dimer models. The viewpoint we take is inspired by mirror symmetry. After an introduction to the combinatorics of dimer models, we will first look at dimers in dynamical systems…
The connection between quiver gauge theories and dimer models has been well studied. It is known that the matter fields of the quiver gauge theories can be represented using the perfect matchings of the corresponding dimer model.We…
In this work, we establish certain enrichments of dual algebraic structures in the setting of monoidal double categories. In more detail, we obtain a tensored and cotensored enrichment of monads in comonads, as well as a tensored and…
We apply the theory of $\alpha$-induction of sectors which we elaborated in our previous paper to several nets of subfactors arising from conformal field theory. The main application are conformal embeddings and orbifold inclusions of SU(n)…
We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a…
We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible $\mathfrak{so}_{2n+1}$-module. These bases are in many ways similar to the FFLV bases for types $A$ and $C$.…
We give combinatorial formulas for F-polynomials in cluster algebras of classical types in terms of the weighted paths in certain directed graphs. As a consequence we prove the positivity of F-polynomials in cluster algebras of classical…
The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. For certain monoids connected with combinatorics, such as the plactic monoid (the monoid…
For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called…