Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1
  standard modules for $\tilde{\mathfrak sl}(\ell+1,\C)$   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
$W(\Lambda)$.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs