Representation theory and combinatorics of classical groups, quantum groups and Hecke algebras

Littlewood-Richardson系数是Schur函数的乘积展开为Schur函数的和的系数，它被描述为Littlewood-Richardson表的组合对象的个数.对于Azenhas给出的Littlewood-Richardson表之间的双射，它实现了反映Schur函数交换性的Littlewood-Richardson系数的对称性，给出了两个组合证明，通过与国王和Azenhas合作，其中一个使用传统的Littlewood-Richardson tableaux，另一个使用新的组合对象，称为蜂巢，最近由Knutson和Tao介绍。

Littlewood-Richardson coefficients, which are the coefficients of products of Schur functions expanded as sums of Schur functions, are described as the numbers of combinatorial objects called Littlewood-Richardson tableaux.For the bijection between Littlewood-Richardson tableaux given by Azenhas, which realizes the symmetry of Littlewood-Richardson coefficients reflecting the commutativity of Schur dunctions, is given two combinatorial proofs, by collaboration with King and Azenhas, one of which using the conventional Littlewood-Richardson tableaux and the other using new combinatorial objects called hives which have been introduced by Knutson and Tao rather recently.