Ghosh, Debarun Spallone, Steven
Published in
Journal of Algebraic Combinatorics

In Ayyer et al. (J Comb Theory Ser A 150:208–232, 2017), the authors characterize the partitions of n whose corresponding representations of Sn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...

Pawlowski, Brendan

To each finite subset of a discrete grid $\mathbb{N}×\mathbb{N}$ (a diagram), one can associate a subvariety of a complex Grassmannian (a diagram variety), and a representation of a symmetric group (a Specht module). Liu has conjectured that the cohomology class of a diagram variety is represented by the Frobenius characteristic of the correspondin...

Giannelli, Eugenio
Published in
Archiv der Mathematik

In this paper we study the vertices of indecomposable Specht modules for symmetric groups. For any given indecomposable non-projective Specht module, the main theorem of the article describes a p-subgroup contained in its vertex. The theorem generalizes and improves an earlier result due to Wildon in [13].

Morse, Jennifer Schilling, Anne

We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of Specht modules associated to permutation diagrams. We show how this crystal framework can be applie...

Billey, Sara Pawlowski, Brendan

Generalizing the notion of a vexillary permutation, we introduce a filtration of $S_{\infty}$ by the number of Edelman-Greene tableaux of a permutation, and show that each filtration level is characterized by avoiding a finite set of patterns. In doing so, we show that if $w$ is a permutation containing $v$ as a pattern, then there is an injection ...

Donkin, Stephen Santana, Ana Paula Yudin, Ivan
Published in
Journal of Algebra

We continue the development of the homological theory of quantum general linear groups previously considered by the first author. The development is used to transfer information to the representation theory of quantised Schur algebras. The acyclicity of induction from some rank-one modules for quantised Borel–Schur subalgebras is deduced. This is u...

Fayers, Matthew Lyle, Sinéad
Published in
Journal of Algebraic Combinatorics

The reducible Specht modules for the Hecke algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {H}_{\mathbb{F},q}(\mathfrak{S}_{n})$\end{document} have been...

Weber, Christian

Ordinary representation theory of the symmetric groups is quite well understood, but there are still many open questions concerning modular representation theory of the symmetric groups. About cohomology of S_n-modules, there is little known as well. This thesis has its starting point where the latter two fields meet. Possibilities of making statem...

Peccati, Giovanni Pycke, Jean-Renaud

It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

Ryom-Hansen, Steen
Published in
Journal of Algebraic Combinatorics

We consider the algebra ℰn(u) introduced by Aicardi and Juyumaya as an abstraction of the Yokonuma–Hecke algebra. We construct a tensor space representation for ℰn(u) and show that this is faithful. We use it to give a basis of ℰn(u) and to classify its irreducible representations.