论文标题
关于增强的还原组（i）：抛物线schur代数和二元性二元性
On enhanced reductive groups (I): Parabolic Schur algebras and the dualities related to degenerate double Hecke algebras
论文作者
论文摘要
$ \ bbc $上的增强的代数$ \ ug $ \ ug $ g = \ gl（v）$是产品品种$ \ gl（v）\ times v $，并具有增强的跨产品。与$ \ ug $的天然张量表示相关，分别有Levi和抛物线代数代数$ \ Mathcal {L} $和$ \ Mathcal {p} $。我们精确地研究了它们的结构，并研究了变体组和代数的增强张量表示。在本课程中，生产了所谓的脱名式双Hecke代数（DDHA）的代数模型，并成为一个有力的实现。 $ \ MATHCAL {L} $和DDHA之间的连接为$ \ gl（v）$的经典表示带来了两个结果： （ii）分支双重性公式。在上述讨论的帮助下，我们进一步获得了抛物线的Schur-weyl二元性，以$ \ ug \ rtimes \ gm $。更重要的是，抛物线schur subergebra结果只有一个块。该代数的cartan不变性是精确确定的。
An enhanced algebraic group $\uG$ of $G=\GL(V)$ over $\bbc$ is a product variety $\GL(V)\times V$, endowed with an enhanced cross product. Associated with a natural tensor representation of $\uG$, there are naturally Levi and parabolic Schur algebras $\mathcal{L}$ and $\mathcal{P}$ respectively. We precisely investigate their structures, and study the dualities on the enhanced tensor representations for variant groups and algebras. In this course, an algebraic model of so-called degenerate double Hecke algebras (DDHA) is produced, and becomes a powerful implement. The connection between $\mathcal{L}$ and DDHA gives rise to two results for the classical representations of $\GL(V)$: (i) A duality between $\GL(V)\times\Gm$ and DDHA where $\Gm$ is the one-dimensional multiplicative group; (ii) A branching duality formula. With aid of the above discussion, we further obtain a parabolic Schur-Weyl duality for $\uG\rtimes \Gm$. What is more, the parabolic Schur subalgebra turns out to have only one block. The Cartan invariants for this algebra are precisely determined.
