论文标题
伸展的Littlewood-Richardson系数的多项式性的简短证明
A Short Proof for the Polynomiality of the Stretched Littlewood-Richardson Coefficients
论文作者
论文摘要
伸展的Littlewood-Richardson系数$ C^{TZ _ {Tλ，Tμ} $由King，Tollu和Toumazet猜想是$ t的多项式功能。后来，Rassart使用Steinberg的公式，Hive条件和Kostant分区函数，以表明$ C^ν_{λ，μ} $确实是变量$ν，λ，μ$的多项式。由Rassart的方法激发，我们使用Steinberg的公式给出了$ C^{Tνλ，Tμ} $多项式性的简短证明，并提供了有关Kostant分区功能的室内复合物的简单论点。
The stretched Littlewood-Richardson coefficient $c^{tν}_{tλ,tμ}$ was conjectured by King, Tollu, and Toumazet to be a polynomial function in $t.$ It was shown to be true by Derksen and Weyman using semi-invariants of quivers. Later, Rassart used Steinberg's formula, the hive conditions, and the Kostant partition function to show a stronger result that $c^ν_{λ,μ}$ is indeed a polynomial in variables $ν, λ, μ$ provided they lie in certain polyhedral cones. Motivated by Rassart's approach, we give a short alternative proof of the polynomiality of $c^{tν}_{tλ,tμ}$ using Steinberg's formula and a simple argument about the chamber complex of the Kostant partition function.
