论文标题
通过BGG类别$ \ MATHCAL {O} $重新访问Jacobi-Trudi身份
Revisiting Jacobi-Trudi identities via the BGG category $\mathcal{O}$
论文作者
论文摘要
通过将Kostka数解释为特殊线性谎言代数的BGG类别中的张量产物倍增性，我们提供了从著名的weyl targe formula衍生而来的经典jacobi-trudi身份的新证明。我们重新建立了偏斜多项式的Jacobi-Trudi膨胀中某些截断的Schur阳性，并获得了jacobi-trudi-type在两个schur多项式产品的产物中相似的截断的schur阳性结果。此外，我们将这些雅各比 - Trudi截断的Schur多项式扩展中的系数解释为BGG类别O中的张量产物多重性。
By interpreting Kostka numbers as tensor product multiplicities in the BGG category O for the special linear Lie algebras, we provide a new proof of the classical Jacobi--Trudi identities for skew Schur polynomials, derived from the celebrated Weyl character formula. We re-establish the Schur positivity of certain truncations in the Jacobi--Trudi expansion of skew Schur polynomials and obtain Schur positivity results for similar truncations in the Jacobi--Trudi-type expansion of the product of two Schur polynomials. Furthermore, we interpret the coefficients in the Schur polynomial expansions of these Jacobi--Trudi truncations as tensor product multiplicities in the BGG category O.
