论文标题
Littlewood-Richardson系数的一些意外特性
Some unexpected properties of Littlewood-Richardson coefficients
论文作者
论文摘要
我们对Littlewood-Richardson系数之间的身份感兴趣，因此对线性GL N（C）的不可值模块的不同张量产品分解进行了比较。一个被定义的分区家族定义了，我们证明了一个稳定性结果，基本上断言，张量产物的分解与近距离分区相关的两个表示不取决于n。给定一个分区$λ$，最多为n，用v n（$λ$）表示相关的简单gl n（c） - 模块。我们推测，如果$λ$接近矩形和$μ$任何分区，则v n（$λ$）$ \ otimes $ v n（$μ$）和v n（$λ$） * $ \ otimes $ v n（$ v n（$μ$）的分解，如果$μ$也是几乎距离的，我们证明了这种猜想，并报告了几项计算机辅助计算，以加强我们的猜想。
We are interested in identities between Littlewood-Richardson coefficients, and hence in comparing different tensor product decompositions of the irreducible modules of the linear group GL n (C). A family of partitions-called near-rectangular-is defined, and we prove a stability result which basically asserts that the decomposition of the tensor product of two representations associated to near-rectangular partitions does not depend on n. Given a partition $λ$, of length at most n, denote by V n ($λ$) the associated simple GL n (C)-module. We conjecture that, if $λ$ is near-rectangular and $μ$ any partition, the decompositions of V n ($λ$) $\otimes$ V n ($μ$) and V n ($λ$) * $\otimes$ V n ($μ$) coincide modulo a mysterious bijection. We prove this conjecture if $μ$ is also near-rectangular and report several computer-assisted computations which reinforce our conjecture.
