论文标题
特殊线性谎言代数
Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras
论文作者
论文摘要
我们提出了一个与斐波那契序列及其概括的一部分等级对称钻石色的分布晶格。这些晶格重新解释并统一对文献中一些未颜色或不同颜色的晶格的描述。我们证明，我们的对称斐波那酸晶格自然会意识到特殊线性谎言代数的某些（通常还原）表示，重量基矢量是晶格元件的重量基矢量，并沿每个晶格的覆盖式挖掘者边缘演奏的代数发生器。我们提供证据表明每个这样的体重基础都具有某些独特的极端特性。我们提供有关晶格红衣的新描述，并排名生成功能，并提供几个猜想/开放问题。在整个过程中，我们与OEI的整数序列建立连接。
We present a family of rank symmetric diamond-colored distributive lattices that are naturally related to the Fibonacci sequence and certain of its generalizations. These lattices re-interpret and unify descriptions of some un- or differently-colored lattices found variously in the literature. We demonstrate that our symmetric Fibonaccian lattices naturally realize certain (often reducible) representations of the special linear Lie algebras, with weight basis vectors realized as lattice elements and Lie algebra generators acting along the covering digraph edges of each lattice. We present evidence that each such weight basis possesses certain distinctive extremal properties. We provide new descriptions of the lattice cardinalities and rank generating functions and offer several conjectures/open problems. Throughout, we make connections with integer sequences from the OEIS.
