论文标题
当前代数的更高级别的BGG互惠
Higher level BGG reciprocity for current algebras
论文作者
论文摘要
我们证明了一个简单的谎言代数的扭曲恋爱关系的厚度和薄项模块之间的扩展正交性。对于每个正整数的扭曲电流代数的伯恩斯坦 - 甘富尔德 - 吉尔夫德（BGG）互惠的较高级别的类似物，该代数恢复了原始的代数（Bennett，Berenstein，Chari，Chari，Ion，Ion，Ion，Khoroshkin，Khoroshkin，Loktev和Manning）作为其级别的一个情况。我们还建立了有关两个版本的纽唑模块的分支属性，并根据对称的多项式对一般级别$ k $限制的Kostka多项式提供了新的解释。
We prove the Ext-orthogonality between thick and thin Demazure modules of the twisted affinization of a simple Lie algebra. This yields a higher level analogue of the Bernstein-Gelfand-Gelfand (BGG) reciprocity for twisted current algebras for each positive integer, that recovers the original one (established by Bennett, Berenstein, Chari, Ion, Khoroshkin, Loktev, and Manning) as its level one case. We also establish the branching properties about the both versions of Demazure modules and provide a new interpretation of general level $k$ restricted Kostka polynomials in terms of symmetric polynomials.
