Related papers: Generalized Schur algebras
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup $GL(m|n)$. Furthermore,…
We obtain a presentation by generators and relations for generalized Schur algebras and their quantizations. This extends earlier results obtained in the type A case. The presentation is compatible with Lusztig's modified form of a…
We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string…
We obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.
Biserial algebras are a classical class in the representation theory of algebras, generalizing Nakayama algebras. They were further generalized by Green and Schroll to multiserial algebras, which share many structural properties with…
Recently, in [18] the authors gave some results on the structure, capability and the Schur multiplier of generalized Heisenberg Lie superalgebra. In this work we try to extend these concepts to the case of generalized Heisenberg Lie…
Schur's Theorem and its generalisation, Baer's Theorem, are distinguished results in group theory, connecting the upper central quotients with the lower central series. The aim of this paper is to generalise these results in two different…
In this work, we provide a q-generalization of flexible algebras and related bialgebraic structures, including center-symmetric (also called antiflexible) algebras, and their bialgebras. Their basic properties are derived and discussed.…
We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies…
Isomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in…
We give explicit presentations by generators and relations of certain generalized Schur algebras (associated with tensor powers of the natural representation) in types B, C, D. This extends previous results in type A obtained by two of the…
We describe a basis of the centre of the Schur algebra which comes from conjugacy classes in the symmetric group via Schur-Weyl duality. We give a combinatorial description of expansions of these basis elements in terms of the basis…
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
We provide a complete classification of the singularities of cluster algebras of finite type with trivial coefficients. Alongside, we develop a constructive desingularization of these singularities via blowups in regular centers over fields…
After reviewing classical Schur-Weyl duality, we present some other contexts which enjoy similar features, relating to Brauer algebras and classical groups.
Given a group $G$ and an integer $n\geq2$ we construct a new group $\tilde{{\cal K}}(G,n)$. Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of…
We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.
We define dual equivalence for any collection of combinatorial objects endowed with a descent set, and we show that giving a dual equivalence establishes the symmetry and Schur positivity of the quasi-symmetric generating function. We give…