Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r, p, n)
Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r, p, n)
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G(r, p, n) 型有理 Cherednik 代数的组合表示理论
DOI：
10.1017/s0013091508000904
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发表时间：
2006
影响因子：
0.7
通讯作者：
Stephen Griffeth
中科院分区：
文献类型：
--
作者：
Stephen Griffeth
摘要本文旨在通过正交函数和交织算子为G（r，p，n）型有理Cherednik代数的$\mathcal{O}$类的组合研究奠定基础.作为第一个应用，本文给出了Gordon定理（原Haiman猜想）在对角余不变环上对群G（r，p，n）（其中r > 1）的类比的一个自包含的初等证明。对p没有任何限制; Vale使用类似于Gordon的技巧证明了p r的结果。由于海曼猜想的组合应用，本文除了关于复反射群的标准事实外，在逻辑上是独立的。主要结果应该是访问数学家工作的代数组合谁是不熟悉的令人印象深刻的范围内使用的想法戈登的证明他的定理。
Abstract This paper aims to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category $\mathcal{O}$ for the rational Cherednik algebra of type G(r, p, n). As a first application, a self-contained and elementary proof of the analogue for the groups G(r, p, n), with r > 1, of Gordon's Theorem (previously Haiman's Conjecture) on the diagonal co-invariant ring is given. No restriction is imposed on p; the result for p ≠ r has been proved by Vale using a technique analogous to Gordon's. Because of the combinatorial application to Haiman's Conjecture, the paper is logically self-contained except for standard facts about complex reflection groups. The main results should be accessible to mathematicians working in algebraic combinatorics who are unfamiliar with the impressive range of ideas used in Gordon's proof of his theorem.