Related papers: Temperley-Lieb Crystals
Guided by consideration of problems in 2 and 3 dimensional lattice model computation, we are led to define a number of new categories, and functors between these categories and the partition category, culminating in the introduction of two…
We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model.…
This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the…
We extend the Framization of the Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$. We first define a natural extension of the classical Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$ and prove that such an…
In previous work, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral…
We prove the Lipman-Zariski conjecture for complex surface singularities of genus one, and also for those of genus two whose link is not a rational homology sphere. As an application, we characterize complex $2$-tori as the only normal…
The centralizer of the image of the diagonal embedding of $U_q(\mathfrak{sl}_2)$ in the tensor product of three irreducible representations is examined in a Schur-Weyl duality spirit. The aim is to offer a description in terms of generators…
Using Langer's construction of Bridgeland stability conditions on normal surfaces, we prove Reider-type theorems generalizing the work done by Arcara-Bertram in the smooth case. Our results still hold in positive characteristic or when…
We give a positive equivariant Littlewood-Richardson rule also discovered independently by Molev. Our proof generalizes a proof by Stembridge of the ordinary Littlewood-Richardson rule. We describe a weight-preserving bijection between our…
B\'ar\'any, Kalai, and Meshulam recently obtained a topological Tverberg-type theorem for matroids, which guarantees multiple coincidences for continuous maps from a matroid complex to d-dimensional Euclidean space, if the matroid has…
In this largely expository article we present an elementary construction of Lusztig's canonical basis in type ADE. The method, which is essentially Lusztig's original approach, is to use the braid group to reduce to rank two calculations.…
In 1992, Wagner proved that the Hadamard product of two totally positive lower triangular Toeplitz matrices is totally positive. In this work, we strengthen this result by establishing total monomial positivity for the Hadamard product of…
A Kazhdan-Lusztig variety is the intersection of a locally-closed Schubert cell with an opposite Schubert variety in a flag variety. We present a linear parametrization of the Schubert cells in the affine type A flag variety via…
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…
Let ${\mathbb{TL}_n^{\! \mathbb Q}} $ be the rational Temperley-Lieb algebra, with loop parameter $ 2 $. In the first part of the paper we study the seminormal idempotents $ E_{ \mathfrak{t}} $ for ${\mathbb{TL}_n^{\! \mathbb Q}}$ for $…
In this paper, we consider affine Deligne-Lusztig varieties $X_w(b)$ and their certain union $X(\mu,b)$ inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne-Lusztig varieties have…
We introduce the Double leaves basis, a combinatorial basis for the Hom spaces between two Bott-Samelson-Soergel bimodules. As an application we give a combinatorial algorithm to find, for any given Weyl or affine Weyl group, the set of…
We introduce a super version of the Littlewood--Richardson rule for super Schur functions over signed alphabets. We give in particular combinatorial interpretations of the super Littlewood--Richardson coefficients using the properties of…
Just as the Temperley-Lieb algebra is a good place to compute the Jones polynomial, the Kauffman bracket skein algebra of a disk with $2k$ colored points on the boundary, each with color $n$, is a good place to compute the $n^{th}$ colored…
We begin an investigation into extending the T1 theorem of David and Journ\'e, and the corresponding cancellation conditions of Stein, to more general pairs of distinct doubling weights. For example, assuming the measures satisfy a…