The real loci of Calogero-Moser spaces, representations of rational Cherednik algebras and the Shapiro conjecture
| dc.creator | Gordon, Iain | |
| dc.creator | Horozov, Emil | |
| dc.creator | Yakimov, Milen | |
| dc.date | 2007-11-27 | |
| dc.date.accessioned | 2026-07-07T08:45:26Z | |
| dc.date.available | 2026-07-07T08:45:26Z | |
| dc.description | We prove a criterion for the reality of irreducible representations of the rational Cherednik algebras H_{0,1}(S_n). This is shown to imply a criterion for the real loci of the Calogero-Moser spaces C_n in terms of the Etingof-Ginzburg finite maps Υ\colon C_n \to C^n/S_n \times C^n/S_n, recovering a result of Mikhin, Tarasov, and Varchenko [MTV2]. As a consequence we obtain a criterion for the real locus of the Wilson's adelic Grassmannian of rank one bispectral solutions of the KP hierarchy. Using Wilson's first parametrisation of the adelic Grassmannian, we give a new proof of a result of [MTV2] on real bases of spaces of quasi polynomials. The Shapiro Conjecture for Grassmannians is equivalent to a special case of our result for Calogero-Moser spaces, namely for the fibres of Υover C^n/S_n \times 0. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0711.4336 | |
| dc.identifier | http://arxiv.org/abs/0711.4336 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142966 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.title | The real loci of Calogero-Moser spaces, representations of rational Cherednik algebras and the Shapiro conjecture | |
| dc.type | text |