论文标题
分段主导序列和环形箭量赫克代数的结合体
Piecewise dominant sequences and the cocenter of the cyclotomic quiver Hecke algebras
论文作者
论文摘要
我们研究了与{\ it nutionary}相关的环环震颤hecke代数我们介绍了一个称为“分段主导序列”的概念，并使用它来构建一些跨越$ r^λ_α$的共同分量的显式均匀元素。我们表明，$ r^λ_α$的关联器的最小度成分由某些klr idempotent $ e（ν）$的图像跨越，其中i^α$中的每个$ν\ in I^α$都是分段的主导力。作为一个应用程序，我们表明重量空间$ l（λ）_ {λ-α} $的最高权重模块$ l（λ）$ by $ \ mathfrak {g}（a）$ nonzero（等效地，$ r^λ_α\ neq 0 $），并且仅在存在$ r.r^λ_α\ neq 0 $）$ ife nece $ inaliase $ inal中。
We study the cocenter of the cyclotomic quiver Hecke algebra $R^Λ_α$ associated to an {\it arbitrary} symmetrizable Cartan matrix $A=(a_{ij})_{i,j}\in I$, $Λ\in P^+$ and $α\in Q_n^+$. We introduce a notion called "piecewise dominant sequence" and use it to construct some explicit homogeneous elements which span the maximal degree component of the cocenter of $R^Λ_α$. We show that the minimal degree components of the cocenter of $R^Λ_α$ is spanned by the image of some KLR idempotent $e(ν)$, where each $ν\in I^α$ is piecewise dominant. As an application, we show that the weight space $L(Λ)_{Λ-α}$ of the irreducible highest weight module $L(Λ)$ over $\mathfrak{g}(A)$ is nonzero (equivalently, $R^Λ_α\neq 0$) if and only if there exists a piecewise dominant sequence $ν\in I^α$.
