Completing the classification of representations of $\mathrm{SL}_n$ with complete intersection invariant ring

Lukas Braun

paper

Completing the classification of representations of $SL_{n}$ with complete intersection invariant ring

arXiv:1812.01978

Abstract

We present a full list of all representations of the special linear group $SL_{n}$ over the complex numbers with complete intersection invariant ring, 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, inbetween 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.

24 pages, various figures, comments are welcome

Completing the classification of representations of SLn​ with complete intersection invariant ring

Abstract

Completing the classification of representations of $SL_{n}$ with complete intersection invariant ring