Harmonic locus and Calogero-Moser spaces
组织者
演讲者
Alexander Veselov
时间
2024年05月20日 12:00 至 13:00
地点
A4-1
摘要
We study the harmonic locus consisting of the monodromy-free Schroedinger operators with rational potential and quadratic growth at infinity. It is known after Oblomkov, that it can be identified with the set of all partitions via Wronskian map for Hermite polynomials. We show that the harmonic locus can also be identified with the subset of the Calogero-Moser space introduced by Wilson, which is invariant under the symplectic action of $\mathbb C^*$. As a corollary, for the multiplicity-free part of the locus we effectively solve the inverse problem for the Wronskian map by describing partition in terms of the spectrum of the corresponding Moser's matrix.
The talk is based on a joint work with Giovanni Felder.
The talk is based on a joint work with Giovanni Felder.