Cyclic Sieving for Generalised Non–Crossing Partitions Associated to Complex Reflection Groups of Exceptional Type
نویسندگان
چکیده
We present the proof of the cyclic sieving conjectures for generalised non-crossing partitions associated to well-generated complex reflection groups due to Armstrong, respectively to Bessis and Reiner, for the 26 exceptional well-generated complex reflection groups. The computational details are provided in the manuscript “Cyclic sieving for generalised non-crossing partitions associated to complex reflection groups of exceptional type — the details” [arχiv:1001.0030].
منابع مشابه
Cyclic Sieving of Noncrossing Partitions for Complex Reflection Groups
We prove an instance of the cyclic sieving phenomenon, occurring in the context of noncrossing parititions for well-generated complex reflection groups.
متن کاملThe M - triangle of generalised non - crossing partitions for the types
The M -triangle of a ranked locally finite poset P is the generating function P u,w∈P μ(u,w)x rk uyrk w, where μ(., .) is the Möbius function of P . We compute the M triangle of Armstrong’s poset of m-divisible non-crossing partitions for the root systems of type E7 and E8. For the other types exceptDn this had been accomplished in the earlier paper “The F -triangle of the generalised cluster c...
متن کاملDecomposition Numbers for Finite Coxeter Groups and Generalised Non-crossing Partitions
Given a finite irreducible Coxeter group W , a positive integer d, and types T1, T2, . . . , Td (in the sense of the classification of finite Coxeter groups), we compute the number of decompositions c = σ1σ2 · · ·σd of a Coxeter element c of W , such that σi is a Coxeter element in a subgroup of type Ti in W , i = 1, 2, . . . , d, and such that the factorisation is “minimal” in the sense that t...
متن کاملEL-Shellability of Generalized Noncrossing Partitions Associated to Well-Generated Complex Reflection Groups
In this article we prove that the poset of m-divisible noncrossing partitions is EL-shellable for every wellgenerated complex reflection group. This was an open problem for type G(d, d, n) and for the exceptional types, for which a proof is given case-by-case. Résumé. Dans cet article nous prouvons que l’ensemble ordonné des partitions non-croisées m-divisibles est ELépluchable (“EL-shellable”)...
متن کاملThe cyclic sieving phenomenon
The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge’s q 1⁄4 1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Pólya–Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues. r 2004 Elsevier Inc. A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011