Intersection of harmonics and Capelli identities for symmetric pairs
| dc.creator | Lee, Soo Teck | |
| dc.creator | Nishiyama, Kyo | |
| dc.creator | Wachi, Akihito | |
| dc.date | 2005-10-03 | |
| dc.date.accessioned | 2026-07-07T06:20:35Z | |
| dc.date.available | 2026-07-07T06:20:35Z | |
| dc.description | We consider a see-saw pair consisting of a Hermitian symmetric pair (G_R, K_R) and a compact symmetric pair (M_R, H_R), where (G_R, H_R) and (K_R, M_R) form real reductive dual pairs in a large symplectic group. In this setting, we get Capelli identities which explicitly represent certain K_C-invariant elements in U(Lie(G)_C) in terms of H_C-invariant elements in U(Lie(M)_C). The corresponding H_C-invariant elements are called Capelli elements. We also give a decomposition of the intersection of O_{2n}-harmonics and Sp_{2n}-harmonics as a module of GL_n = O_{2n} \cap Sp_{2n}, and construct a basis for the GL_n highest weight vectors. This intersection is in the kernel of our Capelli elements. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510033 | |
| dc.identifier | http://arxiv.org/abs/math/0510033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95360 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B35; 22E46 16S32 15A15 | |
| dc.title | Intersection of harmonics and Capelli identities for symmetric pairs | |
| dc.type | text |