AI 中文总结
该研究证明有限变量下斜对称舒尔多项式的标准化形式为洛伦兹型，通过将其实现为舒伯特多项式特化并结合对偶雅可比-崔奇恒等式，推导出斜对称科斯塔数满足沿根方向的对数凹性不等式。
AI 中文摘要
我们证明了Huh、Matherne、Mészáros和St. Dizier的猜想：有限个变量下的每个斜对称舒尔多项式的标准化形式都是洛伦兹型的。我们首先将有限个变量下的每个非零斜对称舒尔多项式实现为舒伯特多项式的特化形式，并证明它是对偶洛伦兹型的。随后，对偶雅可比-崔奇恒等式将其标准化形式与通过矩形补集得到的斜对称舒尔多项式的有限对偶形式对应起来。由此得出，斜对称科斯塔数满足沿根方向的对数凹性不等式。
英文摘要
We prove the conjecture of Huh, Matherne, Mészáros, and St.~Dizier that the normalization of every skew Schur polynomial in finitely many variables is Lorentzian. We first realize every nonzero skew Schur polynomial in finitely many variables as a specialization of a Schubert polynomial and prove that it is dually Lorentzian. The dual Jacobi--Trudi identity then identifies its normalization with the finite dual of a skew Schur polynomial obtained by rectangular complementation. As a consequence, skew Kostka numbers satisfy log-concavity inequalities along the root directions.
