Abstract
We present a full list of all representations of the special linear group SLn 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 SLn 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.
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The author was partially supported by the DFG-Graduiertenkolleg GK1821 “Cohomological Methods in Geometry” at the University of Freiburg.
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BRAUN, L. Completing the Classification of Representations of SLn with Complete Intersection Invariant Ring. Transformation Groups 26, 115–144 (2021). https://doi.org/10.1007/s00031-020-09605-0
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DOI: https://doi.org/10.1007/s00031-020-09605-0