A_n箭图簇的GL重数的组合规则
A combinatorial rule for $GL$-multiplicities of $A_n$-quiver loci
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中文总结 AI 辅助
研究A类箭图轨道闭包坐标环中不可约GL表示重数问题，提出首个对任意定向均有效的正组合规则，利用带晶体结构的组合对象最高权元计算重数，补充了复形簇情形的隐式描述。
中文摘要 AI 辅助
我们给出了A类箭图轨道闭包的坐标环中不可约GL表示重数的首个正组合规则，该规则对箭图的任意定向均有效。此前，针对复形簇这一特殊情形，De Concini与Strickland在20世纪80年代初的工作给出了这些重数的隐式描述。我们规则中的组合对象带有晶体结构，其最高权元可计算这些重数。
英文摘要
We give the first positive combinatorial rule for the multiplicities of irreducible $GL$-representations in the coordinate rings of type $A$ quiver orbit closures, valid for every orientation of the quiver. Previously, for the special case of varieties of complexes, work of De Concini--Strickland in the early 1980s gave an implicit description of these multiplicities. The combinatorial objects in our rule carry a crystal structure whose highest-weight elements compute these multiplicities.
