论文标题
$Δ$ - 苏格林格品种和Hall-Littlewood多项式
$Δ$-Springer varieties and Hall-Littlewood polynomials
论文作者
论文摘要
$δ$ -springer品种是莱文森（Levinson），Woo和作者引入的Springer纤维的概括，它们与代数Compinatorics与Delta猜想有连接。我们证明了$δ$ - 苏格林格品种的共同体学环的分级弗罗贝尼乌斯特征的正式霍尔小木膨胀公式。我们通过将frobenius特征解释为有限字段$ \ mathbb {f} _q $的计数点，并将$δ$ -springer综艺的分区分为杂交纤维的副本。作为一种特殊情况，我们的证明方法为Haglund，Rhoades和Shimozono的公式提供了几何含义，用于在$ t = 0 $的三角洲猜想中的对称功能的Hall-Littlewood扩展。
The $Δ$-Springer varieties are a generalization of Springer fibers introduced by Levinson, Woo, and the author that have connections to the Delta Conjecture from algebraic combinatorics. We prove a positive Hall-Littlewood expansion formula for the graded Frobenius characteristic of the cohomology ring of a $Δ$-Springer variety. We do this by interpreting the Frobenius characteristic in terms of counting points over a finite field $\mathbb{F}_q$ and partitioning the $Δ$-Springer variety into copies of Springer fibers crossed with affine spaces. As a special case, our proof method gives a geometric meaning to a formula of Haglund, Rhoades, and Shimozono for the Hall-Littlewood expansion of the symmetric function in the Delta Conjecture at $t=0$.
