Alpha-determinant cyclic modules and Jacobi polynomials

Kazufumi Kimoto, Sho Matsumoto, Masato Wakayama

We study the cyclic $U({\mathfrak{gl}}_n)$-module generated by the $l$-th power of the $\alpha$-determinant. When $l$ is a non-negative integer, for all but finite exceptional values of $…