Related papers: Hook Interpolations

Let $V$ be a finite-dimensional vector space over the field with $p$ elements, where $p$ is a prime number. Given arbitrary $\alpha,\beta\in \mathrm{GL}(V)$, we consider the semidirect products $V\rtimes\langle \alpha\rangle$ and…

This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in $k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as some of…

This paper concerns representations of the integral general linear group. The extension groups $Ext^2$ between any pair of hook Weyl modules are determined via a detailed study of cyclic generators and relations associated to certain…

The first detailed comparison of the low-momentum interaction V_{low k} with G matrices is presented. We use overlaps to measure quantitatively the similarity of shell-model matrix elements for different cutoffs and oscillator frequencies.…

Let $k$ be an infinite field of positive characteristic. We determine all homomorphisms between Weyl modules for $GLn(k)$, where one of the partitions is a hook. As a consequence we obtain a nonvanishing result concerning homomorphisms…

We determine the multiplicities of irreducible summands in the symmetric and the exterior squares of hook representations of symmetric groups over an algebraically closed field of characteristic zero.

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…

Several bases of the Garsia-Haiman modules for hook shapes are given, as well as combinatorial decomposition rules for these modules. These bases and rules extend the classical ones for the coinvariant algebra of type $A$. We also give a…

We consider the decomposition into irreducible components of the external power $\Lambda^p(\mathbb{C}^m\otimes \mathbb{C}^n)$ regarded as a $\operatorname{GL}_m\times\operatorname{GL}_n$-module. Skew Howe duality implies that the Young…

This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…

Using polyadic MV algebras, we show that many predicate many valued logics have the interpolation property.

The fusion procedure provides a way to construct new solutions to the Yang-Baxter equation. In the case of the symmetric group the fusion procedure has been used to construct diagonal matrix elements using a decomposition of the Young…

Given a representation V of a group G, there are two natural ways of defining a representation of the group algebra k[G] in the external power V^{\wedge m}. The set L(V) of elements of k[G] for which these two ways give the same result is a…

In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such…

For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are…

When we deal with $H^{\infty}$, it is known that $c_0-$interpolating sequences are interpolating and it is sufficient to interpolate idempotents of $\ell_\infty$ in order to interpolate the whole $\ell_\infty$. We will extend these results…

Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra $A$ which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper we…

We consider Vinberg $\theta$-groups associated to a cyclic quiver on $r$ nodes. Let $K$ be the product of general linear groups associated to the nodes, acting naturally on $V = \oplus \text{Hom}(V_i, V_{i+1})$. We study the harmonic…

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.