论文标题
副定制的nilpotent轨道和明确的字符公式，用于模块上的模块。
Subregular nilpotent orbits and explicit character formulas for modules over affine Lie algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为一个简单的有限尺寸复杂谎言代数，让$ \ wideHat {\ mathfrak {g}} $为相应的affine lie lie代数。 KAC和WakiMoto观察到，在某些情况下，字符公式中的系数具有简单的最高权重$ \ wideHat {\ Mathfrak {\ Mathfrak {g}} $ - 模块是界限的，要么由重量的线性函数给出。我们使用kazhdan-lusztig理论来解释并概括了这一观察结果，通过计算$ q = 1 $的某些（抛物线抗抛物线）仿射逆Kazhdan-lusztig多项式的值。特别是，我们获得了一些$ \ wideHat {\ mathfrak {g}} $ - 负整数$ k $的模块时，当$ \ mathfrak g $属于$ d_n $，$ e_6 $，$ e_6 $，$ e_7 $，$ e_7 $，$ e_8 $ and $ k \ geq asslant -2，-2，-6-6，-46，-46-6，-46， - Wakimoto。 该计算取决于对与亚规则细胞相对应的仿射Hecke代数上抗球形模块的细胞商中规范基础的明确描述。我们还介绍了在弹簧分辨率上的Equivariant Cooherent Sheaves派生类别中相应对象的明确描述，它们对应于某个与所谓的非交换性Springer分辨率相关的特定$ t $结构中的不可减至的对象。
Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a simple highest weight $\widehat{\mathfrak{g}}$-module are either bounded or are given by a linear function of the weight. We explain and generalize this observation using Kazhdan-Lusztig theory, by computing values at $q=1$ of certain (parabolic) affine inverse Kazhdan-Lusztig polynomials. In particular, we obtain explicit character formulas for some $\widehat{\mathfrak{g}}$-modules of negative integer level $k$ when $\mathfrak g$ is of type $D_n$, $E_6$, $E_7$, $E_8$ and $k \geqslant -2, -3, -4, -6$ respectively, as conjectured by Kac and Wakimoto. The calculation relies on the explicit description of the canonical basis in the cell quotient of the anti-spherical module over the affine Hecke algebra corresponding to the subregular cell. We also present an explicit description of the corresponding objects in the derived category of equivariant coherent sheaves on the Springer resolution, they correspond to irreducible objects in the heart of a certain $t$-structure related to the so called non-commutative Springer resolution.
