Sebastian Debus (UiT - The Arctic University of Norway)

Higher Specht polynomials and invariant sums of squares

We will consider the representation and invariant theory of real reflection groups with focus on the combinatorial representation theory of the symmetric group $S_n$, the signed symmetric group $B_n$ and $D_n$. Furthermore, we show an application of complexity reduction using symmetry. We use the higher Specht polynomials for sums of squares versus non-negativity questions in equivariant situations and provide explicit examples for invariants under the groups $S_n, B_n$ and $D_n$ in low dimensions. arXiv: 2011.09997.