Correction factors for Kac-Moody groups and t-deformed root multiplicities
Correction factors for Kac-Moody groups and t-deformed root multiplicities
复制标题
Kac-Moody 群和 t 变形根多重数的校正因子
DOI：
10.1007/s00209-019-02419-1
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发表时间：
2019
影响因子：
0.8
通讯作者：
Ian Whitehead
中科院分区：
文献类型：
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作者：
Dinakar Muthiah;Anna Puskas;Ian Whitehead
研究了p进Kac-Moody群理论中出现的Kac-Moody根系的修正因子。在仿射型中，这个因子是已知的，它的显式计算是麦克唐纳常数项猜想的内容。校正因子的数据可以编码为以正虚根为索引的多项式集合。在这些多项式的求值为根多重，因此我们认为是在变形。我们推广了Peterson算法和Berman-Moody公式来计算根多重。因此我们推导出的基本性质。
We study a correction factor for Kac–Moody root systems which arises in the theory ofp-adic Kac–Moody groups. In affine type, this factor is known, and its explicit computation is the content of the Macdonald constant term conjecture. The data of the correction factor can be encoded as a collection of polynomialsindexed by positive imaginary roots. Atthese polynomials evaluate to the root multiplicities, so we considerto be at-deformation of. We generalize the Peterson algorithm and the Berman–Moody formula for root multiplicities to compute. As a consequence we deduce fundamental properties of.