Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}\left(\widehat{sl}_2\right)$
Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}\left(\widehat{sl}_2\right)$
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关于椭圆代数最高权模的注释 ${cal A}_{q,p}left(widehat{sl}_2 ight)$
DOI：
10.1143/ptps.118.1
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Hong Yan
中科院分区：
文献类型：
--
作者：
O. Foda;K. Iohara;M. Jimbo;R. Kedem;T. Miwa;Hong Yan
讨论了最近定义的椭圆代数${calA}{q，p}(widehat{sl}2)$的最高权模的构造，并对其提出了几个猜想.这些模是通过运算符$L$的分量对最高权重向量的作用生成的。通过顶点算子与L算子的对易关系，我们引入了顶点算子$\Phi$和$\Psi^*$。我们给出了$L$-和$\Phi$-算子的排序规则，并找到了由它们生成的线性无关向量个数的一个上界，它与$\widehat{sl}_2$-模的已知特征一致。
We discuss a construction of highest weight modules for the recently defined elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, and make several conjectures concerning them. The modules are generated by the action of the components of the operator $L$ on the highest weight vectors. We introduce the vertex operators $\Phi$ and $\Psi^*$ through their commutation relations with the $L$-operator. We present ordering rules for the $L$- and $\Phi$-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of $\widehat{sl}_2$-modules.