论文标题
堆，晶体和预约代数模块
Heaps, crystals, and preprojective algebra modules
论文作者
论文摘要
修复一个简单的半胶结谎言代数。我们研究水晶$ b（nλ）$，为$λ$是主要的小重量，而$ n $是自然数字。一方面，$ b（nλ）$可以通过与$λ$相关的堆的高度$ n $反向平面分区来实现。另一方面，我们使用此堆来定义一个模块，这是基础dynkin颤动的前注位代数。利用斋藤和野蛮林利的工作，我们通过该模块的$ n $副本的Quiver Grassmannian的不可约组件认识到$ b（nλ）$。在本文中，我们描述了$ b（nλ）$的这两个模型之间的明确射击，并证明我们的两者培养产生了晶体的同构。我们的主要几何工具是Nakajima的张量Quiver品种。
Fix a simply-laced semisimple Lie algebra. We study the crystal $ B(nλ)$, were $λ$ is a dominant minuscule weight and $n$ is a natural number. On one hand, $B(nλ)$ can be realized combinatorially by height $n$ reverse plane partitions on a heap associated to $λ$. On the other hand, we use this heap to define a module over the preprojective algebra of the underlying Dynkin quiver. Using the work of Saito and Savage-Tingley, we realize $B(nλ)$ via irreducible components of the quiver Grassmannian of $n$ copies of this module. In this paper, we describe an explicit bijection between these two models for $B(nλ)$ and prove that our bijection yields an isomorphism of crystals. Our main geometric tool is Nakajima's tensor product quiver varieties.
