论文标题
B型的单一表示有理Cherednik代数和晶体组合学
Unitary representations of type B rational Cherednik algebras and crystal combinatorics
论文作者
论文摘要
我们将2级Fock空间的晶体组合学与B ROWICATION CHEDERNIK代数的单一不可还原表示的分类来研究单位性代数，以研究单位性在抛物线限制下的行为。首先，我们表明，这种代数的任何有限维统一不可约的表示都由一个由一个组件中的矩形分区组成的两部分和另一个组件中的空分区组成。这是可以从蒙塔拉尼（Montarani）和埃丁福（Etingof-Stoica）定理推导的结果的新证明。其次，我们表明卸下盒子的晶体操作员保留了单位性的组合条件，并且抛物线限制函数对晶体的分类将不可约合的统一表示向单一表示。第三，我们找到了统一表示的支持。
We compare crystal combinatorics of the level 2 Fock space with the classification of unitary irreducible representations of type B rational Cherednik algebras to study how unitarity behaves under parabolic restriction. First, we show that any finite-dimensional unitary irreducible representation of such an algebra is labeled by a bipartition consisting of a rectangular partition in one component and the empty partition in the other component. This is a new proof of a result that can be deduced from theorems of Montarani and Etingof-Stoica. Second, we show that the crystal operators that remove boxes preserve the combinatorial conditions for unitarity, and that the parabolic restriction functors categorifying the crystals send irreducible unitary representations to unitary representations. Third, we find the supports of the unitary representations.
