  We determine the composition factors of the polynomial representation of
DAHA, conjectured by M. Kasatani. We reduce the determination of composition
factors of polynomial representations of DAHA to the determination of the
composition factors of the Weyl module $W^{(1^n)}$ for the $v$-Schur algebra.
By using the LLT-Ariki type theorem of $v$-Schur algebra proved by
Varagnolo-Vasserot, we determine the composition factors of $W^{(1^n)}$ by
calculating the upper global basis and crystal basis of Fock space of
$U_q(\hat{\mf{sl}}_\ell)$.

Representation Theory;Quantum Algebra