论文标题
无限二元矩阵上的二元性和双重性
Duality and bicrystals on infinite binary matrices
论文作者
论文摘要
已知具有有限型A型双晶结构的有限二进制矩阵集。我们首先回顾了这种经典的结构，解释了它如何简短证明科斯特卡多项式和一维总和之间的平等以及2M-x Pitman变换的自然概括。接下来，我们表明，一旦引入了无限二元矩阵家庭的相关形式主义，这是一种更普遍的现象的特殊情况。事实证明，每个这样的矩阵家族都具有kac-moody双晶体和由经典根系定义的三级晶体结构。此外，我们给出了这些多晶的明确分解，让人想起产生cauchy身份的字符的分解。
The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums together with a natural generalisation of the 2M -- X Pitman transform. Next, we show that, once the relevant formalism on families of infinite binary matrices is introduced, this is a particular case of a much more general phenomenon. Each such family of matrices is proved to be endowed with Kac-Moody bicrystal and tricrystal structures defined from the classical root systems. Moreover, we give an explicit decomposition of these multicrystals, reminiscent of the decomposition of characters yielding the Cauchy identities.
