最高权Macdonald和Jack多项式
Highest weight Macdonald and Jack Polynomials
摘要：
最低朗道能级粒子的分数量子霍尔态可用多元多项式描述。在旋转群下，不可压缩液体状态在球体上描述时是完全不变的。激发准粒子/准空穴态是旋转群下多重态的成员，一般来说，多重态中存在一个非平凡的最高权成员，所有的态都可以从该成员构造出来。在文献中提出的一些试验状态属于经典的对称多项式族。在本文中，我们研究的Macdonald和Jack多项式的最高权状态。对于Macdonald多项式，它是定义最高权条件的提升角动量算子的（q，t）-变形。通过参数的特殊化，我们得到了最高权Jack多项式的分类。我们的结果是有效的情况下，阶梯和矩形分区索引的多项式。
英文摘要：
Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
