Fundamental invariants of tensors, Latin hypercubes, and rectangular Kronecker coefficients

Abstract

We study polynomial SL-invariants of tensors, mainly focusing on fundamental invariants which are of smallest degrees. In particular, we prove that certain 3-dimensional analogue of the Alon--Tarsi conjecture on Latin cubes considered previously by Bürgisser and Ikenmeyer, implies positivity of (generalized) Kronecker coefficients at rectangular partitions and as a result provides values for degree sequences of fundamental invariants.

arXiv commentTheorem 1.1 is improved, new sec. 8.3 and Theorem 8.12 are added in v2. The final version (after referee's comments) to appear in IMRN