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

In the previous paper, the authors proved linear independence of the combinatorial spanning set for standard $C_\ell^{(1)}$-module $L(k\Lambda_0)$ by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type…

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of the type $A_\ell^{(1)}$. We find a combinatorial basis of Feigin-Stoyanovsky's type subspace $W(\Lambda)$ given in terms of difference and initial conditions. Linear independence of the…

In this paper we construct combinatorial bases of Feigin-Stoyanovsky's type subspaces of standard modules for level $k$ affine Lie algebra $C_\ell^{(1)}$. We prove spanning by using annihilating field $x_\theta (z)^{k+1}$ of standard…

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of type $A_\ell^{(1)}$. Suppose we're given a $\mathbb Z$-gradation of the corresponding simple finite-dimensional Lie algebra ${\mathfrak g}={\mathfrak g}_{-1}\oplus{\mathfrak g}_0 \oplus…

Let $\gtl$ be an affine Lie algebra of type $D_{\ell}^{(1)}$ and $L(\Lambda)$ its standard module with a highest weight vector $v_{\Lambda}$. For a given $\Z$-gradation $\gtl = \gtl_{-1} + \gtl_0 + \gtl_1$, we define Feigin-Stoyanovsky's…

In this paper we construct bases of standard (i.e. integrable highest weight) modules $L(\Lambda)$ for affine Lie algebra of type $B_2\sp{(1)}$ consisting of semi-infinite monomials. The main technical ingredient is a construction of…

Feigin-Stoyanovsky's type subspace $W(\Lambda)$ of a standard $\tilde{{\mathfrak g}}$-module $L(\Lambda)$ is a $\tilde{{\mathfrak g}}_1$-submodule of $L(\Lambda)$ generated by the highest-weight vector $v_\Lambda$, where $\tilde{{\mathfrak…

Certain combinatorial bases of Feigin-Stoyanovsky's type subspaces of level k standard modules for affine Lie algebra sl(r,C)\sptilde are parametrized by (k,r)-admissible configurations. In this note we use Capparelli-Lepowsky-Milas' method…

Let $\widetilde{\mathfrak g}$ be an affine Lie algebra of type $D_4^{(1)}$ and $L(\Lambda)$ its standard module of level $k$ with highest weight vector $v_{\Lambda}$. We define Feigin--Stoyanovsky's type subspace as…

We consider principal subspaces $W_{L(k\Lambda_0)}$ and $W_{N(k\Lambda_0)}$ of standard module $L(k\Lambda_0)$ and generalized Verma module $N(k\Lambda_0)$ at level $k\geq 1$ for affine Lie algebra of type $B_2^{(1)}$. By using the theory…

J.~Lepowsky and R.~L.~Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via vertex operator constructions of standard (i.e. integrable highest weight) representations of affine Kac-Moody Lie algebras.…

In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $L^2(\mathbb R^d)$. Our proof is based on a simple argument from the…

Let $d$ be a positive fundamental discriminant, and let $\mathcal{C}_{d}$ be the set of isomorphism classes of cubic number fields of discriminant $d$. For each $K \in \mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ with…

For a lattice \Lambda in the complex plane, let K_{\Lambda} be the field of \Lambda-elliptic functions. For two relatively prime integers p (respectively q) greater than 1, consider the endomorphisms \psi (resp. \phi) of K_{\Lambda} given…

Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and $R=\mathbb{K}[x_1,x_2,...x_n]$ the polynomial ring in $n$ variables over $\mathbb K.$ We study bases of the free $R$-module $W_n(\mathbb{K})$ of all…

Let $(x_1,y_1),\ldots,(x_n,y_n)$ be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system \begin{equation}\notag \begin{split} x'&= axy + bx\\ y'&= cxy + dy, \end{split} \end{equation} where…

We introduce the notion of Hilbert $C^*$-module independence: Let $\mathscr{A}$ be a unital $C^*$-algebra and let $\mathscr{E}_i\subseteq \mathscr{E},\,\,i=1, 2$, be ternary subspaces of a Hilbert $\mathscr{A}$-module $\mathscr{E}$. Then…

The study of linear independence of $L(k, \chi)$ for a fixed integer $k>1$ and varying $\chi$ depends critically on the parity of $k$ vis-\`a-vis $\chi$. This has been investigated by a number of authors for Dirichlet characters $\chi$ of a…

We construct a quasi-particle basis of the integrable highest weight module of highest weight $3\Lambda_0$ for the twisted affine Lie algebra of type $A_2^{(2)}$ in the principal realization. More specifically, by introducing the concept of…

Feigin-Stoyanovsky's type subspaces for affine Lie algebras of type $C_\ell^{(1)}$ have monomial bases with a nice combinatorial description. We describe bases of whole standard modules in terms of semi-infinite monomials obtained as "a…