Composition Factors of Polynomial Representation of DAHA and Crystallized Decomposition Numbers
Composition Factors of Polynomial Representation of DAHA and Crystallized Decomposition Numbers
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DAHA多项式表示的组成因素与结晶分解数
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发表时间：
2006
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通讯作者：
Naoya Enomoto
中科院分区：
文献类型：
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作者：
Naoya Enomoto
我们确定了M.笠谷我们将DAHA多项式表示的合成因子的确定归结为v-Schur代数的Weyl模W^{（1^n）}的合成因子的确定.利用Varagnolo-Vasserot证明的$v$-Schur代数的LLT-Ariki型定理，通过计算$U_q（hat{mf{sl}}_ell）$的Fock空间的上整体基和晶体基来确定$W^{（1^n）}$的组成因子。
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 $U_q(hat{mf{sl}}_ell)$.