Related papers: Recurrence relations for characters of affine Lie …

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…

Exact sequences of Feigin-Stoyanovsky's type subspaces for affine Lie algebra $\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$ lead to systems of recurrence relations for formal characters of those subspaces. By solving the corresponding…

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…

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…

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…

We use vertex operator algebras and intertwining operators to study certain substructures of standard $A_1^{(1)}$--modules, allowing us to conceptually obtain the classical Rogers--Ramanujan recursion. As a consequence we recover…

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.

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…

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…

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…

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…

Using certain results for the vertex operator algebras associated with affine Lie algebras we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an affine Lie algebra. As an application we…

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…

Generalizing some of our earlier work, we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine Lie algebras of types A, D and E, and also of certain related spaces. As a…

We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their…

We study the principal subspaces, introduced by B. Feigin and A. Stoyanovsky, of the level 1 standard modules for $\hat{\goth{sl}(l+1)}$ with $l \geq 2$. In this paper we construct exact sequences which give us a complete set of recursions…

Using completions of certain universal enveloping algebras, we provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex…

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…

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…

In this note we explain, in terms of finite dimensional representations of Lie algebras $\mathfrak{sp}_{2\ell}\subset\mathfrak{sl}_{2\ell}$, a combinatorial coincidence of difference conditions in two constructions of combinatorial bases…