Related papers: An algorithm for semistandardising homomorphisms

We seek solutions $u\in\R^n$ to the semilinear elliptic partial difference equation $-Lu + f_s(u) = 0$, where $L$ is the matrix corresponding to the Laplacian operator on a graph $G$ and $f_s$ is a one-parameter family of nonlinear…

A mapping of $k$-bit strings into $n$-bit strings is called an $(\alpha,\beta)$-map if $k$-bit strings which are more than $\alpha k$ apart are mapped to $n$-bit strings that are more than $\beta n$ apart. This is a relaxation of the…

We prove and generalize a conjecture in arXiv:1610.0474(4) about the asymptotics of $\frac{1}{\sqrt{n!}} f^{\lambda/\mu}$, where $f^{\lambda/\mu}$ is the number of standard Young tableaux of skew shape $\lambda/\mu$ which have stable limit…

Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for non-degenerate Brauer algebras. We generalise their construction to a wider class of…

In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a…

Let $\nabla^\lambda$ denote the Schur functor labelled by the partition $\lambda$ and let $E$ be the natural representation of $\mathrm{SL}_2(\mathbb{C})$. We make a systematic study of when there is an isomorphism $\nabla^\lambda…

We construct a moduli scheme for semistable pre-$\D$-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-$\D$-modules are to be viewed as regular holonomic $\D$-modules with `level structure'.…

For any odd $n$, we describe a smooth minimal (i.e. obtained by adding an irreducible hypersurface) compactification $\tilde S_n$ of the quasi-projective homogeneous variety $S_{n}=PGL(n+1)/SL(2)$ that parameterizes the rational normal…

The irreducible representations of symmetric groups can be realized as certain graded pieces of invariant rings, equivalently as global sections of line bundles on partial flag varieties. There are various ways to choose useful bases of…

We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting of the classes that naturally arise from the Bialynicki-Birula decomposition of the Hessenberg varieties. We give an explicit combinatorial…

The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…

Let $G$ be a finite group of order $n$ and let $M$ be a $G$-module. We construct groups $H_*^\varkappa(G,M)$ for which $H_k^\varkappa (G,M^{tw}) \cong H^{n-k-1}_\lambda(G,M),$ where $M^{tw}$ is a twisting of a $G$-module $M$ defined in…

We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer…

Let $(M,\omega)$ be a closed symplectic manifold and $\textup{Ham}(M,\omega)$ the group of Hamiltonian diffeomorphisms of $(M,\omega)$. Then the Seidel homomorphism is a map from the fundamental group of $\textup{Ham}(M,\omega)$ to the…

We provide a proof that every Schubert variety of a semi-infinite flag variety is projectively normal. This gives us an interpretation of a Demazure module of a global Weyl module of a current Lie algebra as the (dual) space of the space of…

Let $M^K_n$ be the moduli space of framed $K$-instantons with instanton number $n$ when $K$ is a compact simple Lie group of classical type. Due to Donaldson's theorem, its scheme structure is given by the regular locus of a GIT quotient of…

We construct semi-orthogonal decompositions on triangulated categories of parabolic sheaves on certain kinds of logarithmic schemes. This provides a categorification of the decomposition theorems in Kummer flat K-theory due to Hagihara and…

This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…

We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring $A=\mathbb Z[q^{1/2},q^{-1/2}]$ where $q$ is an indeterminate) using…

In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g. the Helmholtz…