论文标题
通用角色因团结根源而扭曲
Universal characters twisted by roots of unity
论文作者
论文摘要
Littlewood的经典结果给出了Schur函数在一组变量上的分解，由原始的$ t $ th $ THONE的统一根“扭曲”，其特征在于索引分区的核心和商。虽然有些忽视，但事实证明，它是对称群体的特征理论，环状筛分现象，多个对称函数的重要工具。最近，对组的字符的类似分解$ \ mathrm {o}（2n，\ mathbb {c}）$，$ \ mathrm {sp}（2n，2n，\ mathbb {c}）$ and $ \ mathrm {so}（so}（2n+1，+1，\ 1，\ mathbb {c c} c。我们将这些结果提升到通用字符的水平，这可以使证据更简单，而分解的结构更加透明。我们的方法还允许Ciucu和Krattenthaler最初发现的不同性质的某些分解的普遍性扩展，并由Ayyer和Behrend概括。
A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected, it has proved to be an important tool in the character theory of the symmetric group, the cyclic sieving phenomenon, plethysms of symmetric functions and more. Recently, similar factorisations for the characters of the groups $\mathrm{O}(2n,\mathbb{C})$, $\mathrm{Sp}(2n,\mathbb{C})$ and $\mathrm{SO}(2n+1,\mathbb{C})$ were obtained by Ayyer and Kumari. We lift these results to the level of universal characters, which has the benefit of making the proofs simpler and the structure of the factorisations more transparent. Our approach also allows for universal character extensions of some factorisations of a different nature originally discovered by Ciucu and Krattenthaler, and generalised by Ayyer and Behrend.
