Related papers: Linear independence for $C_\ell^{(1)}$ by using $C…

We construct quasi-particle bases of principal subspaces of standard modules $L(\Lambda)$, where $\Lambda=k_0\Lambda_0+k_j\Lambda_j$, and $\Lambda_j$ denotes the fundamental weight of affine Lie algebras of type $B_l^{(1)}$, $C_l^{(1)}$,…

In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…

We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability…

Let $\Lambda \subset \mathbb R^n$ be an algebraic lattice, coming from a projective module over the ring of integers of a number field $K$. Let $\mathcal Z \subset \mathbb R^n$ be the zero locus of a finite collection of polynomials such…

We construct combinatorial bases of principal subspaces of standard modules of level $k \geq 1$ with highest weight $k\Lambda_0$ for the twisted affine Lie algebras of type $A_{2l-1}^{(2)}$, $D_l^{(2)}$, $E_6^{(2)}$ and $D_4^{(3)}$. Using…

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove…

In this article we investigate different forms of multiplicative independence between the sequences $n$ and $\lfloor n \alpha \rfloor$ for irrational $\alpha$. Our main theorem shows that for a large class of arithmetic functions $a, b…

We use combinatorial description of bases of Feigin-Stoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types $A_\ell^{(1)}$ and $D_4^{(1)}$ to obtain character formulas. These descriptions naturally lead…

For $S_k$, the space of cusp forms of weight $k$ for the full modular group, we first introduce periods on $S_k$ associated to symmetric square $L$-functions. We then prove that for a fixed natural number $n$, if $k$ is sufficiently large…

We construct particle basis for Feigin-Stoyanovsky's type subspaces of level $1$ standard $\tilde{\mathfrak{sl}}_{\ell+1}(\mathbb{C})$-modules. From the description we obtain character formulas.

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

B. Feigin and A. Stoyanovsky found the basis of semi-infinite monomials in standard $\widehat{\mathfrak{sl}}_2'$-module $L_{(0, 1)}$ with Lefschetz formula for the corresponding flag variety. These semi-infinite monomials are constructed by…

This is the first of a series of papers studying combinatorial (with no ``subtractions'') bases and characters of standard modules for affine Lie algebras, as well as various subspaces and ``coset spaces'' of these modules. In part I we…

The main result of this paper is a combinatorial description of a basis of standard level 1 module for the twisted affine Lie algebra $A_2^{(2)}.$ This description also gives two new combinatorial identities of G\"ollnitz (or…

This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups are linearly independent whenever the associated twisted…

Let X be an L_1-predual space and let K be a countable linearly independent subset of the extreme points of its closed dual ball. It is shown that if the norm-closed linear span Y of K is w^*-closed in X^*, then Y is the range of a…

Let $L$ be a Lie algebra of Block type over $\C$ with basis $\{L_{\alpha,i}\,|\,\alpha,i\in\Z\}$ and brackets $[L_{\alpha,i},L_{\beta,j}]=(\beta(i+1)-\alpha(j+1))L_{\alpha+\beta,i+j}$. In this paper, we shall construct a formal distribution…

Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we…

This paper examines linear independence of shearlet systems. This property has already been studied for wavelets and other systems such as, for instance, for Gabor systems. In fact, for Gabor systems this problem is commonly known as the…

We study time-independent radially symmetric first-order solitons in a CP(2) model interacting with an Abelian gauge field whose dynamics is controlled by the usual Maxwell term. In this sense, we develop a consistent first-order framework…