标题： 克罗内克系数、晶体和双表 显示英文标题

标题： Kronecker Coefficients, Crystals, and Bitableaux

摘要： 克罗内克系数的组合解释可能是什么样子的呢？ 我们引入了一类称为双表的组合对象，我们认为它们是一个自然的候选，并提出了一个纯粹的组合问题，如果解决这个问题，将给出克罗内克系数的组合解释。 我们在这一问题上取得了一些部分进展——足以提取出在单项基下克罗内克乘积的组合展开式。 我们还解释了在这个框架下，寻找克罗内克系数的组合解释可以被视为寻找RSK和对偶RSK插入算法的推广。 显示英文摘要

摘要： What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natural candidate, and we formulate a purely combinatorial problem which if resolved would give a combinatorial interpretation of the Kronecker coefficients. We make some partial progress on this problem -- enough to extract a combinatorial expansion for a Kronecker product of Schur functions in the monomial basis. We also explain how in this framework finding a combinatorial interpretation for Kronecker coefficients can be thought of as looking for a generalization of the RSK and dual RSK insertion algorithms.