Related papers: Matroidal Schur Algebras

We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras $\mathcal{R}^\Lambda_n$ of type $A$ when $e=0$ (the linear quiver) or $e\ge n$. We show that these algebras are quasi-hereditary graded cellular algebras…

Let $r \leqslant n$ be nonnegative integers, and let $N = \binom{n}{r} - 1$. For a matroid $M$ of rank $r$ on the finite set $E = [n]$ and a partial field $k$ in the sense of Semple--Whittle, it is known that the following are equivalent:…

In this paper, we generalize Schur-Weyl duality and Morita Theorem on associative algebras to those on associative $H$-pseudoalgebras. Meanwhile, we get a plenty of associative $H$-pseudoalgebras over a cocommutative Hopf algebra $H$.

A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…

Let $\mathtt{k}$ be an algebraically closed field of characteristic zero. Let $\mathfrak{g} $ be a finite dimensional classical simple Lie superalgebra over $\mathtt{k}$ or $\mathfrak{g} l(m,n)$. In the case that $\mathfrak{g} $ is a…

We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although this result is in principle known, the…

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…

We propose an extension of the theory of parity sheaves, which allows for non-locally constant sheaves along strata. Our definition is tailored for proving the existence of (proper, quasihereditary, etc) stratifications of…

Given a quasi-hereditary superalgebra $A$, the first author and R. Muth have defined generalized Schur bi-superalgebras $T^A(n)$ and proved that these algebras are again quasi-hereditary. In particular, $T^A(n)$ comes with a family of…

The aim of this paper is to define and study some quasi-hereditary covers for higher zigzag algebras. We will show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and…

Up to Morita equivalence, every quasi-hereditary algebra is the dual algebra of a directed bocs or coring. From the bocs, an exact Borel subalgebra is obtained. In this paper a characterisation of exact Borel subalgebras arising in this way…

We extend Schur-Weyl duality to an arbitrary level $l \geq 1$, the case $l=1$ recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke…

This paper aims at developing a "local--global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the…

Given two quasi-hereditary algebras, their tensor product is quasi-hereditary. In this article, we show that given two exact Borel subalgebras for these quasi-hereditary algebras, their tensor product is an exact Borel subalgebra. Moreover,…

Motivated by the study of (m,n)-quasitilted algebras, which are the piecewise hereditary algebras obtained from quasitilted algebras of global dimension two by a sequence of (co)tiltings involving n-1 tilting modules and m-1 cotilting…

The ADR algebra $R_A$ of a finite-dimensional algebra $A$ is a quasihereditary algebra. In this paper we study the Ringel dual $\mathcal{R}(R_A)$ of $R_A$. We prove that $\mathcal{R}(R_A)$ can be identified with $(R_{A^{op}})^{op}$, under…

We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra…

We introduce the notion of quantum Schur (or $q$-Schur) superalgebras. These algebras share certain nice properties with $q$-Schur algebras such as base change property, existence of canonical $\mathbb Z[v,v^{-1}]$-bases, and the duality…

In this paper we consider how the \nabla-, \Delta- and global dimensions of a quasi-hereditary algebra are interrelated. We first consider quasi-hereditary algebras with simple preserving duality and such that if \mu < \lambda then \nabla…

We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal superalgebras, generalizing the well known result of Vasserot-Varagnolo [VV96] to the super case.