论文标题
o o的类别谎言谎言代数
Category O for Takiff Lie algebras
论文作者
论文摘要
我们研究类别$ \ Mathcal {O} $ for Takiff Lie代数$ \ Mathfrak {G} \ otimes \ Mathbb {C} [C} [ε]/（ε^2）$，其中$ \ Mathfrak {g Mathfrak {g} $是lie Algebra，是$ algebraic Group的lie algebra cop $ mathbbb} $。我们将此类别分解为某些子类别的直接总和，并使用抛物线诱导函数和扭曲函数的类似物为BGG类别$ \ MATHCAL {O} $来证明这些子类别之间的等价。然后，我们使用这些等价来计算Verma模块中简单模块的组成倍数，以BGG类别中的组成倍数$ \ Mathcal {O} $用于还原的$ \ Mathfrak {g} $的还原subergebras。我们得出结论，组成的多重性是根据kazhdan-lusztig多项式给出的。
We study category $\mathcal{O}$ for Takiff Lie algebras $\mathfrak{g} \otimes \mathbb{C}[ε]/(ε^2)$ where $\mathfrak{g}$ is the Lie algebra of a reductive algebraic group over $\mathbb{C}$. We decompose this category as a direct sum of certain subcategories and use an analogue of parabolic induction functors and twisting functors for BGG category $\mathcal{O}$ to prove equivalences between these subcategories. We then use these equivalences to compute the composition multiplicities of the simple modules in the Verma modules in terms of composition multiplicities in the BGG category $\mathcal{O}$ for reductive subalgebras of $\mathfrak{g}$. We conclude that the composition multiplicities are given in terms of the Kazhdan-Lusztig polynomials.
