仿射FPF W-图的分子与渐近行贝辛格对应
Molecules of an affine FPF $W$-graph and a labelled row-Beissinger reconstruction
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中文总结 AI 辅助
该研究针对仿射A型，证明仿射无不动点对合经双循环截断和有限行Beissinger插入可渐近恢复AMBC的表型与支配权，并完成Γₙ^m分子的分类。
中文摘要 AI 辅助
Kazhdan-Lusztig W-图编码Hecke代数的胞腔结构，其双向连通分支称为分子。在有限A型中，Robinson-Schensted对应描述胞腔与分子，Beissinger的行插入构造与对合相关的标准表。在仿射A型中，仿射矩阵球构造（AMBC）为仿射置换分配一对表型及一个支配权，Marberg引入由仿射无不动点对合索引的仿射FPF W-图。我们证明，对仿射无不动点对合，完全双循环截断后接有限行Beissinger插入可渐近恢复其公共AMBC表型及支配权；还将Γₙ^m的双向边与AMBC下的对偶等价变换对应，得到其分子的分类。
英文摘要
Kazhdan--Lusztig $W$-graphs encode the cell structure of Hecke algebras, while their bidirected connected components are called molecules. In finite type~$A$, the Robinson--Schensted correspondence describes cells and molecules, and Beissinger's row insertion constructs the common tableau associated with an involution. In affine type~$A$, the affine matrix-ball construction (AMBC) assigns an affine permutation a pair of tabloids together with a dominant weight, and Marberg introduced affine fixed-point-free (FPF) $W$-graphs indexed by affine FPF involutions. We classify and enumerate the molecules of Marberg's $\m$-type affine FPF $W$-graph $Γ_n^{\m}$ and show that molecules with the same AMBC shape have isomorphic underlying simple bidirected graphs. We also prove that labelled complete-cycle row-Beissinger truncations recover the full AMBC datum of an affine FPF involution.
发表机构
- South China Normal University（华南师范大学）
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