论文标题
在环形库克氏菌和cocenter的循环schur代数上的痕量形成
Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras
论文作者
论文摘要
We define a unified trace form $τ$ on the cyclotomic Hecke algebras $\mathscr{H}_{n,K}$ of type $A$, which generalize both Malle-Mathas' trace form on the non-degenerate version (with Hecke parameter $ξ\neq 1$) and Brundan-Kleshchev's trace form on the degenerate version.我们使用半正态基础理论来构建$ \ mathscr {h} _ {n，k} $相对于表格的双基碱基。 We also construct an explicit basis for the cocenter (i.e., the $0$th Hochschild homology) of the corresponding cyclotomic Schur algebra, which shows that the cocenter has dimension independent of the ground field $K$, the Hecke parameter $ξ$ and the cyclotomic parameters $Q_1,\cdots,Q_\ell$.
We define a unified trace form $τ$ on the cyclotomic Hecke algebras $\mathscr{H}_{n,K}$ of type $A$, which generalize both Malle-Mathas' trace form on the non-degenerate version (with Hecke parameter $ξ\neq 1$) and Brundan-Kleshchev's trace form on the degenerate version. We use seminormal basis theory to construct a pair of dual bases for $\mathscr{H}_{n,K}$ with respect to the form. We also construct an explicit basis for the cocenter (i.e., the $0$th Hochschild homology) of the corresponding cyclotomic Schur algebra, which shows that the cocenter has dimension independent of the ground field $K$, the Hecke parameter $ξ$ and the cyclotomic parameters $Q_1,\cdots,Q_\ell$.
