  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 ${\mathfrak g}={\mathfrak
g}_{-1}\oplus{\mathfrak g}_0 \oplus {\mathfrak g}_1$; then we also have the
induced $\mathbb Z$-gradation of the affine Lie algebra $$\tilde{\mathfrak
g}=\tilde{\mathfrak g}_{-1} \oplus \tilde{\mathfrak g}_0 \oplus
\tilde{\mathfrak g}_1.$$
  Let $L(\Lambda)$ be a standard module of level 1. Feigin-Stoyanovsky's type
subspace $W(\Lambda)$ is the $\tilde{\mathfrak g}_1$-submodule of $L(\Lambda)$
generated by the highest-weight vector $v_\Lambda$,
$$W(\Lambda)=U(\tilde{\mathfrak g}_1)\cdot v_\Lambda\subset L(\Lambda).$$ We
find a combinatorial basis of $W(\Lambda)$ given in terms of difference and
initial conditions. Linear independence of the generating set is proved
inductively by using coefficients of intertwining operators. A basis of
$L(\Lambda)$ is obtained as an ``inductive limit'' of the basis of
$W(\Lambda)$.

Quantum Algebra;Representation Theory