Parking structures: Fuss analogs
Parking structures: Fuss analogs
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停车结构：大惊小怪的类似物
DOI：
10.1007/s10801-013-0494-1
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发表时间：
2012
影响因子：
0.8
通讯作者：
B. Rhoades
中科院分区：
文献类型：
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作者：
B. Rhoades
对于任何不可约实反射群W，考克塞特数h，阿姆斯特朗，赖纳，作者介绍了一对值得称为W-停车位的模块，它概括了停车函数的A型概念，并推测了它们之间的关系。在本文中，我们给出了它们构造的 Fuss 类比。对于 Fuss 参数 k≥1，我们定义一对值得称为 k-W-停车位的模块，并推测它们之间的关系。我们证明了对于有限反射群的每个无限族 ABCDI 的猜想的最弱版本，以及特殊情况下更强版本的证明。每当我们最弱的猜想成立时，我们就有以下推论。对于任一k-W-停车空间的特征，有一个简单的公式。由于Krattenthaler和Müller，我们恢复了循环筛分结果，它给出了对k-W-非交叉分区的广义旋转作用的循环结构。当Wi是晶体学时，任一k-W-停车空间对Wi的限制同构于Won有限的作用torusQ/(kh+1)Q，其中Q是根格。
For any irreducible real reflection groupWwith Coxeter numberh, Armstrong, Reiner, and the author introduced a pair of-modules which deserve to be calledW-parking spaceswhich generalize the type A notion of parking functions and conjectured a relationship between them. In this paper we give a Fuss analog of their constructions.For a Fuss parameterk≥1, we define a pair of-modules which deserve to be calledk-W-parking spacesand conjecture a relationship between them. We prove the weakest version of our conjectures for each of the infinite families ABCDI of finite reflection groups, together with proofs of stronger versions in special cases. Whenever our weakest conjecture holds forW, we have the following corollaries.There is a simple formula for the character of eitherk-W-parking space.We recover a cyclic sieving result due to Krattenthaler and Müller which gives the cycle structure of a generalized rotation action onk-W-noncrossing partitions.WhenWis crystallographic, the restriction of eitherk-W-parking space toWis isomorphic to the action ofWon the finite torusQ/(kh+1)Q, whereQis the root lattice.