Hall–Littlewood Plane Partitions and KP
Hall–Littlewood Plane Partitions and KP
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DOI：
10.1093/imrn/rnp028
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发表时间：
2008-09
影响因子：
1
通讯作者：
O. Foda;M. Wheeler
中科院分区：
文献类型：
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作者：
O. Foda;M. Wheeler
MacMahon的经典生成函数的随机平面分区，这是有关舒尔多项式，最近被Vuletic扩展到一个生成函数的加权平面分区，这是有关霍尔-利特尔伍德多项式，并进一步到一个有关的麦克唐纳多项式。利用Jing提出的带电自由费米子的单参数变形，我们得到了Hall-Littlewood扩张的Fock空间导数。限制的平面分区到一个有限的平方基地，我们表明，由此产生的生成函数，是一个评估的KP-功能。
MacMahon's classic generating function of random plane partitions, which is related to Schur polynomials, was recently extended by Vuletic to a generating function of weighted plane partitions that is related to Hall-Littlewood polynomials, , and further to one related to Macdonald polynomials, . Using Jing's one-parameter deformation of charged free fermions, we obtain a Fock space derivation of the Hall-Littlewood extension. Confining the plane partitions to a finite square base, we show that the resulting generating function, , is an evaluation of a -function of KP.