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Related papers: Some new decomposable Specht modules

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In preprint alg-geom/9708009 we have constructed a (ten-dimensional) symplectic desingularization of the moduli space of rank-two torsion-free semistable sheaves on a $K3$, with trivial determinant and second Chern class equal to 4. In the…

Algebraic Geometry · Mathematics 2007-05-23 Kieran G. O'Grady

We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs,…

Representation Theory · Mathematics 2018-01-23 Yury A. Neretin

We give a full classification, in terms of periodic skew diagrams, of irreducible semisimple modules in category O for the degenerate double affine Hecke algebra of type A which can be realized as submodules of Verma modules.

Representation Theory · Mathematics 2016-08-09 Martina Balagovic

Let n be a positive integer and let p be a prime. Suppose that we take a partition of n, and obtain another partition by moving a node from one row to a shorther row. Carter and Payne showed that if the p-residue of the removed and added…

Representation Theory · Mathematics 2009-02-16 H. Ellers , J. Murray

Fix a compact 4-dimensional manifold with self-dual 2nd Betti number one and with a given symplectic form. This article proves the following: The Frechet space of tamed almost complex structures as defined by the given symplectic form has…

Symplectic Geometry · Mathematics 2017-08-15 Clifford Henry Taubes

In the 1980s Dr\'ezet and Le Potier realized moduli spaces of Gieseker-semistable sheaves on $\mathbb{P}^2$ as what are now called quiver moduli spaces. We discuss how this construction can be understood using t-structures and exceptional…

Algebraic Geometry · Mathematics 2018-12-10 Andrea Maiorana

To the integral symplectic group Sp(2g,Z) we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the…

Geometric Topology · Mathematics 2013-03-26 Wilberd van der Kallen , Eduard Looijenga

We classify all homomorphisms between Weyl modules for SL_3(k) when k is an algebraically closed field of characteristic at least three, and show that the Hom-spaces are all at most one-dimensional. As a corollary we obtain all…

Representation Theory · Mathematics 2007-05-23 Anton Cox , Alison Parker

Recently Pelayo-V\~{u} Ngoc classified semitoric integrable systems in terms of five symplectic invariants. Using this classification we define a family of metrics on the space of semitoric integrable systems. The resulting metric space is…

Symplectic Geometry · Mathematics 2017-04-17 Joseph Palmer

Via simulation, we discover and prove curious new Euclidean properties and invariants of the Poncelet family of harmonic polygons.

Metric Geometry · Mathematics 2022-09-30 Ronaldo Garcia , Dan Reznik , Pedro Roitman

Four $\ZZ_+$-bigraded complexes with the action of the exceptional infinite-dimensional Lie superalgebra E(3,6) are constructed. We show that all the images and cokernels and all but three kernels of the differentials are irreducible…

Mathematical Physics · Physics 2014-01-17 Victor G. Kac , Alexei Rudakov

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…

Category Theory · Mathematics 2022-03-03 Driss Bennis , Juan Ramón García Rozas , Hanane Ouberka , Luis Oyonarte

In this paper, we will prove that the 2-category (2-SGp) of symmetric 2-groups and 2-category ($\cR$-2-Mod) of $\cR$-2-modules(\cite{5}) have enough projective objects, respectively.

Category Theory · Mathematics 2010-06-25 Fang Huang , Shao-Han Chen , Wei Chen , Zhu-Jun Zheng

Considering Schur positivity of differences of plethysms of homogeneous symmetric functions, we introduce a new relation on integer partitions. This relation is conjectured to be a partial order, with its restriction to one part partitions…

Combinatorics · Mathematics 2022-04-04 Étienne Tétreault

Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect…

Representation Theory · Mathematics 2018-10-03 Yu Jiang

Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…

Computer Vision and Pattern Recognition · Computer Science 2026-01-09 Zachary Grey , Nicholas Fisher , Andrew Glaws

We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…

Commutative Algebra · Mathematics 2016-01-26 Martin Kohls , Mufit Sezer

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions…

Group Theory · Mathematics 2024-01-09 Michael Bate , Gerhard Röhrle , Damian Sercombe , David I. Stewart

Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible characters of symmetric groups (again of degree 66 or more)…

Representation Theory · Mathematics 2009-03-18 Mark Wildon

Let $q$ be a prime power, $G=GL_n(q)$ and let $U\leqslant G$ be the subgroup of (lower) unitriangular matrices in $G$. For a partition $\lambda$ of $n$ denote the corresponding unipotent Specht module over the complex field $\C$ for $G$ by…

Representation Theory · Mathematics 2013-04-18 Qiong Guo