Invariant theory for singular $\alpha$-determinants

Kazufumi Kimoto, Masato Wakayama

From the irreducible decompositions' point of view, the structure of the cyclic $G{L}_n$-module generated by the $\alpha$-determinant degenerates when $\alpha =\pm \frac{1}{k}(1\le k\le n-1)$. I…