论文标题
应急表和广义的Littlewood-Richardson系数
Contingency tables and the generalized Littlewood-Richardson coefficients
论文作者
论文摘要
Littlewood-Richardson系数$ c^λ_{μν} $给出了多项式多项式$ {\ rm gl} _n $ -presentation $ f^μ_n\ otime f^f^f^f^n $的张量。在本文中，我们将这些系数推广到合理表示的$ r $折张量产品，并提供了一种使用统计应急表的模拟来计算它们的新方法。我们证明了特殊情况，其中我们的方法将其减少到具有规定边缘的统计意外表。最后，我们将结果从一般线性组扩展到正交组和符号群。
The Littlewood-Richardson coefficients $c^λ_{μν}$ give the multiplicity of an irreducible polynomial ${\rm GL}_n$-representation $F^λ_n$ in the tensor product of polynomial representations $F^μ_n\otimes F^ν_n$. In this paper, we generalize these coefficients to an $r$-fold tensor product of rational representations, and give a new method for computing them using an analogue of statistical contingency tables. We demonstrate special cases in which our method reduces to counting statistical contingency tables with prescribed margins. Finally, we extend our result from the general linear group to both the orthogonal and symplectic groups.
