We present a full list of all representations of the special linear group SL_n over the complex numbers with complete intersection invariant ring of homological dimension greater than or equal to two, completing the classification of Shmelkin. For this task, we combine three techniques. Firstly, the graph method for invariants of SL_n developed by the author to compute invariants, covariants and explicit forms of syzygies. Secondly, a new algorithm for finding a monomial order such that a certain basis of an ideal is a Gröbner basis with respect to this order, in between usual Gröbner basis computation and computation of the Gröbner fan. Lastly, a modification of an algorithm by Xin for MacMahon partition analysis to compute Hilbert series.

我们提供了一个完整的特殊线性群SL _n在复数上的所有表示的完整列表，其中均等维数大于或等于2的完全相交不变环，从而完成了Shmelkin的分类。对于此任务，我们结合了三种技术。首先，作者开发了SL _n不变量的图方法，以计算不变量，协变量和显性形式的sysygie。其次，在通常的格罗布纳基础计算和格罗布纳风扇的计算之间，找到一种新的算法来找到单项式，使得理想的某个基础相对于该阶为格罗布纳基础。最后，Xin对MacMahon分区分析的算法进行了修改，以计算希尔伯特级数。