无限二元矩阵上的对偶与双晶
Duality and bicrystals on infinite binary matrices
摘要：
已知给定大小的有限二进制矩阵的集合具有有限型A双晶体结构。我们首先回顾这一经典的建设，解释它如何产生一个简短的证明之间的平等Kostka多项式和一维总和与自然推广的2 M- X皮特曼变换。接下来，我们表明，一旦相关的形式主义家庭的无限二元矩阵介绍，这是一个特殊的情况下，一个更普遍的现象。证明了每一类矩阵都具有由经典根系定义的Kac-Moody双晶和三晶结构。此外，我们给出了一个明确的分解这些多晶体，让人想起分解的字符产生的柯西身份。
英文摘要：
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.
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