Related papers: Combinatorial bases of Feigin-Stoyanovsky's type s…

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…

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 $\tilde{\mathfrak g}$ 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…

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 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…

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…

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…

In this note we prove 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 subspace $W(k\Lambda_0)$…

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…

By using the known description of combinatorial bases for Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebra $\mathfrak{sl}(l+1,\mathbb{C})^{\widetilde{}}$, as well as certain intertwining operators between…

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…

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…

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…

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 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 $B_l^{(1)}$, $C_l^{(1)}$,…

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.

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…

Using the bases of principal subspaces for twisted affine Lie algebras except $A_{2l}^{(2)}$ by Butorac and Sadowski, we construct bases of the highest weight modules of highest weight $k\Lambda_0$ and parafermionic spases for the same…

We use the theory of vertex operator algebras and intertwining operators to obtain systems of q-difference equations satisfied by the graded dimensions of the principal subspaces of certain level k standard modules for \hat{\goth{sl}(3)}.…

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.…