Nguyen, Viet Anh
Published in
Journal of Algebraic Combinatorics

We prove two explicit formulae for one-part double Hurwitz numbers with completed 3-cycles. We define “combinatorial Hodge integrals” from these numbers in the spirit of the celebrated ELSV formula. The obtained results imply some explicit formulae and properties of the combinatorial Hodge integrals.

Conder, Marston Hubard, Isabel O’Reilly-Regueiro, Eugenia Pellicer, Daniel
Published in
Journal of Algebraic Combinatorics

In this paper we describe a construction for finite abstract chiral 4-polytopes with Schläfli type {3,3,k}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{3,3,k\}$$\en...

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].

Giannelli, Eugenio
Published in
Archiv der Mathematik

The Foulkes module \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H^{(a^b)}}$$\end{document} is the permutation module for the symmetric group Sab given by the action...

Bogomolov, Fedor Rovinsky, Marat
Published in
Open Mathematics

Let ψ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension ≥ 3 over a field. Let H be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_\psi $ of the set ψ. Suppose that H contains the projective group and an arbitrary self-bijection of ψ transformi...

Wan, Jinkui Wang, Weiqiang
Published in
Journal of Algebraic Combinatorics

We introduce a spin analogue of Kostka polynomials and show that these polynomials enjoy favorable properties parallel to the Kostka polynomials. Further connections of spin Kostka polynomials with representation theory are established.

Comes, Jonathan Kujawa, Jonathan R.
Published in
Journal of Algebraic Combinatorics

Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne’s category admits a unique nontrivial family of modified trace functions. Such modified trace functions have already proven to be interesting in both low-dimensional topology and representation theory. We also i...

Gill, Christopher C.
Published in
Archiv der Mathematik

The family of Young modules which are periodic has been determined in Hemmer and Nakano (J Algebra 254:422–440, 2002). We determine the period of all periodic Young modules in all characteristics. In particular, the period is dependent only on the characteristic. We calculate minimal projective resolutions of periodic Young modules in weight one bl...

Lim, K.J. Tan, K.M.

10.1007/s00013-011-0342-2 / Archiv der Mathematik / 98 / 2 / 99-104

Lim, Kay Jin Tan, Kai Meng
Published in
Archiv der Mathematik

Let M be a left module for the Schur algebra S(n, r), and let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${s \in \mathbb{Z}^+}$$\end{document} . Then \documentclass...