论文标题
最大年轻亚组球形函数的阳性特性
Positivity properties for spherical functions of maximal Young subgroups
论文作者
论文摘要
令$ s_k \ times s_ {n-k} $为对称组的最大年轻子组$ s_n $。我们引入了一个基础$ {\ MATHCAL B} _ {n，k} $ for coset space $ s_n/s_k \ times s_ {n-k} $自然地由标准的Young tableaux组成的$ n $ box，大多数两行，最多是$ k $ boxes，以及第二checiond of二行的最多$ k $ box。基础$ {\ MATHCAL B} _ {n，k} $具有类似于根系的阳性属性，并且有一个coptosition系列的coset空间，其中每个项都由它包含的基本元素所跨越。我们证明了相关的Gelfand对的球形函数是$ {\ Mathcal B} _ {n，k} $的非负线性组合。
Let $S_k \times S_{n-k}$ be a maximal Young subgroup of the symmetric group $S_n$. We introduce a basis ${\mathcal B}_{n,k}$ for the coset space $S_n/S_k \times S_{n-k}$ that is naturally parametrized by the set of standard Young tableaux with $n$ boxes, at most two rows, and at most $k$ boxes in the second row. The basis ${\mathcal B}_{n,k}$ has positivity properties that resemble those of a root system, and there is a composition series of the coset space in which each term is spanned by the basis elements that it contains. We prove that the spherical functions of the associated Gelfand pair are nonnegative linear combinations of the ${\mathcal B}_{n,k}$.
