论文标题
关于Coxeter转换的相互作用和行李射击
On the interaction of the Coxeter transformation and the rowmotion bijection
论文作者
论文摘要
令$ p $为有限的poset和$ l $ $ p $的订单理想分布晶格。令$ρ$表示$ p $的订单理想的行两本，被视为排列矩阵和$ c $ $ c $ the Coxeter矩阵的发病率代数$ kl $ $ l $。然后，我们显示标识$（ρ^{ - 1} c）^2 = id $，就像Sam Hopkins最初猜想一样。最近，人们注意到，RowMotion Boovastion是一个特殊的情况，即对任何Auslander常规代数都存在的更一般的培训$ r $。这激发了研究一般Auslander常规代数的级别两者和Coxeter基质的相互作用。对于来自$ n $ -presentation有限代数的高级Auslander代数，我们表明$（r^{ - 1} c）^2 = id $如果$ n $均匀且$（r^{ - 1} C+id）
Let $P$ be a finite poset and $L$ the associated distributive lattice of order ideals of $P$. Let $ρ$ denote the rowmotion bijection of the order ideals of $P$ viewed as a permutation matrix and $C$ the Coxeter matrix for the incidence algebra $kL$ of $L$. Then we show the identity $(ρ^{-1} C)^2=id$, as was originally conjectured by Sam Hopkins. Recently it was noted that the rowmotion bijection is a special case of the much more general grade bijection $R$ that exists for any Auslander regular algebra. This motivates to study the interaction of the grade bijection and the Coxeter matrix for general Auslander regular algebras. For the class of higher Auslander algebras coming from $n$-representation finite algebras we show that $(R^{-1} C)^2=id$ if $n$ is even and $(R^{-1}C+id)^2=0$ when $n$ is odd.
