On syzygies of highest weight orbits
| dc.creator | Gorodentsev, A. L. | |
| dc.creator | Khoroshkin, A. S. | |
| dc.creator | Rudakov, A. N. | |
| dc.date | 2006-02-15 | |
| dc.date | 2007-02-03 | |
| dc.date.accessioned | 2026-07-07T07:44:29Z | |
| dc.date.available | 2026-07-07T07:44:29Z | |
| dc.description | We consider the graded space $R$ of syzygies for the coordinate algebra $A$ of projective variety $X=G/P$ embedded into projective space as an orbit of the highest weight vector of an irreducible representation of semisimple complex Lie group $G$. We show that $R$ is isomorphic to the Lie algebra cohomology $H=H^\bdot(\Lt,\CC)$, where $\Lt$ is graded Lie subalgebra of the graded Lie s-algebra $L=L_1\oplus\Lt$ Koszul dual to $A$. We prove that the isomorphism identifies the natural associative algebra structures on $R$ and $H$ coming from their Koszul and Chevalley DGA resolutions respectively. For subcanonically embedded $X$ a Frobenius algebra structure on the syzygies is constructed. We illustrate the results by several examples including the computation of syzygies for the Plücker embeddings of grassmannians $\Gr(2,N)$. | |
| dc.description | 35 pages, some references and acknowledgments are added to the previous version | |
| dc.identifier | https://arxiv.org/abs/math/0602316 | |
| dc.identifier | http://arxiv.org/abs/math/0602316 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123212 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | 51P05; 18G10,14F05,13A50 | |
| dc.title | On syzygies of highest weight orbits | |
| dc.type | text |