K(E9) from K(E10)
K(E9) from K(E10)
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K(E9) 从 K(E10)
DOI：
10.1088/1126-6708/2007/06/051
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发表时间：
2006
影响因子：
5.4
通讯作者：
Jakob Palmkvist
中科院分区：
文献类型：
--
作者：
Axel Kleinschmidt;H. Nicolai;Jakob Palmkvist
我们在隐藏的卡茨 - 穆迪对称性的背景下，分析了在将D = 11超引力理论约化到二维时空后切空间结构群的M理论推广。研究了所得的无限维“R对称”群K(E9)对从K(E10)继承的某些非忠实的有限维旋量表示的作用。我们详细解释了这些表示如何与K(E9)内的某些有限余维理想相关（我们明确给出了这些理想），以及已知的以及新的有限维“广义完整群”如何作为K(E9)被这些理想所除的商而出现。根据E9和K(E9)在二维时空的最大超引力场的圈代数实现，这些商被证明对应于（广义的）赋值映射，这与[1]中的先前结果一致。现在的突出问题是，K(E10)的相关非忠实表示是否可以用类似的方式理解。
We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D = 11 supergravity theory to two space-time dimensions in the context of hidden Kac-Moody symmetries. The action of the resulting infinite-dimensional `R symmetry' group K(E9) on certain unfaithful, finite-dimensional spinor representations inherited from K(E10) is studied. We explain in detail how these representations are related to certain finite codimension ideals within K(E9), which we exhibit explicitly, and how the known, as well as new finite-dimensional `generalised holonomy groups' arise as quotients of K(E9) by these ideals. In terms of the loop algebra realisations of E9 and K(E9) on the fields of maximal supergravity in two space-time dimensions, these quotients are shown to correspond to (generalised) evaluation maps, in agreement with previous results of [1]. The outstanding question is now whether the related unfaithful representations of K(E10) can be understood in a similar way.