Related papers: Sign sequences and decomposition numbers
New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families…
A detailed description is given for the construction of the deformation of the N=2 supersymmetric $\alpha=1$ KdV-equation, leading to the recursion operator for symmetries and the zero-th Hamiltonian structure; the solution to a…
An orthogonal decomposition problem of Lie algebras over the complex numbers has been studied since the 1980s. It has many applications and relations to other areas of mathematics and sciences. In this paper, we consider this decomposition…
For a graph $G$ on $v(G)$ vertices let $m_k(G)$ denote the number of matchings of size $k$, and consider the partition function $M_{G}(\lambda)=\sum_{k=0}^nm_k(G)\lambda^k$. In this paper we show that if $G$ is a $d$--regular graph and…
We show that the general L\'{e}vy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group, ${\bf R}$. The formula of de Finetti corresponds to coboundaries. Kolmogorov's processes…
The existence of a decomposition space with a dendritic structure of a topological space $(\{0,1\}^\Lambda ,\tau_{0}^\Lambda )$ is discussed. Here, $\Lambda $ is any set with the cardinal number $\succ \aleph , \{0,1\}^{\Lambda }=\{\varphi…
The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using…
In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay…
Let $\frak g$ be the finite dimensional simple Lie algebra associated to an indecomposable and symmetrizable generalized Cartan matrix $C=(a_{ij})_{n\times n}$ of finite type and let $\frak d$ be a finite dimensional Lie algebra related to…
Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the…
Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with diameter at least three and standard module $V$. We introduce two direct sum decompositions of $V$. We call these the displacement decomposition for $\Gamma$ and the split…
We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…
The ring of symmetric functions $\Lambda$, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the…
Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition…
Brundan and Kleshchev introduced graded decomposition numbers for representations of cyclotomic Hecke algebras of type $A$, which include group algebras of symmetric groups. Graded decomposition numbers are certain Laurent polynomials,…
The purpose of this note is to give an insertion scheme proof of the formula, $$p_\mu = \sum_{\lambda\vdash k} \chi^\lambda(\mu)s_\lambda,\formula$$ where $p_\mu$ is the power sum symmetric function, $s_\lambda$ is the Schur function and…
In this article some explicit estimates on the decay of the convolutive inverse of a sequence are proved. They are derived from the functional calculus for Sobolev algebras. Applications include localization in spline-type spaces and…
The goal of this paper is threefold. First, we describe the notion of dissociation for closed subgroups of the group of permutations on a countably infinite set and explain its numerous consequences on unitary representations…
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas…
The notion of denominator vectors can be extended to all generic basis elements of upper cluster algebras in a natural way. Under a weakened version of generic pairing assumption, we provide a representation-theoretic interpretation for…