论文标题
Hecke代数的总非负和诱发符号字符
Total nonnegativity and induced sign characters of the Hecke algebra
论文作者
论文摘要
令$ \ mathfrak s _ {[i，j]} $为对称组$ \ mathfrak s_n $的子组，由相邻换位$（i，i，i+1），\ dotsc，（j-1，j）$，假设$ 1 \ leq i <j-1，j）$。我们提供了一个组合规则，用于评估$ \ sum_ {w \ in \ sum_ {w \ in \ mathfrak s _ {[i，j]}} t_w $的所有元素的type-a $ a $ a $ hecke代数$ h_n（q）$。这包括Kazhdan-Lusztig基础的某些元素的评估$ c'_w（q）$。
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 $1 \leq i < j \leq n$. 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.
