Naslov
Singular BGG complexes for the symplectic case

Autori
Mrđen, Rafael

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Prirodoslovno-matematički fakultet - Matematički odsjek

Mjesto
Zagreb

Datum
23.10

Godina
2017

Stranica
Xv + 107

Mentor
Pandžić, Pavle ; Souček, Vladimír

Ključne riječi
BGG ; Resolution ; Homogeneous bundles ; Invariant differential operators ; Generalized Verma modules ; Symplectic group, Lagrangian Grassmannian ; Penrose transform

Sažetak
Let G be a semisimple Lie group and P its parabolic subgroup. It is well known that any finite-dimensional simple G-module allows a resolution by invariant differential operators acting between direct sums of homogeneous bundles over the generalized flag manifold G/P. Such a resolution is called the Bernstein- Gelfand-Gelfand (BGG for short) resolution. In the dual setting, this corresponds to the resolution of a finite-dimensional simple g- module by direct sums of generalized Verma modules, which is also called the BGG resolution. Modules in the resolution have a regular infinitesimal character. Using the Penrose transform, we construct analogues of such resolutions in certain singular infinitesimal characters, in the holomorphic geometric setting, for type C. We take G to be the symplectic group, P its |1|-graded parabolic subgroup, so that G/P is the Lagrangian Grassmannian. We explicitly describe the operators in the resolution, and determine their order. We prove the exactness of the constructed complex over the big affine cell.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA