Let \({\mathfrak {S}}_{[i,j]}\) be the subgroup of the symmetric group \({\mathfrak {S}}_n\) generated by adjacent transpositions \((i,i+1), \dotsc , (j-1,j)\), assuming \(1 \le i < j \le n\). We give a combinatorial rule for evaluating induced sign characters of the type A Hecke algebra \(H_n(q)\) at all elements of the form \(\sum _{w \in {\mathfrak {S}}_{[i,j]}} T_w\) and at all products of such elements. This includes evaluation at some elements \(C'_w(q)\) of the Kazhdan–Lusztig basis.

中文翻译：

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Hecke 代数的全非负性和诱导符号特征

令\({\mathfrak {S}}_{[i,j]}\)是由相邻换位产生的对称群\({\mathfrak {S}}_n\)的子群\((i,i+ 1), \dotsc , (j-1,j)\)，假设\(1 \le i < j \le n\)。我们给出一个组合规则用于评估的类型的诱导的符号字符甲Hecke代数的\（H_n（Q）\）在表格中的所有元素\（\总和_ {瓦特\在{\ mathfrak {S}} _ {[我,j]}} T_w\)以及这些元素的所有乘积。这包括对 Kazhdan-Lusztig 基的某些元素\(C'_w(q)\)的评估。