On syzygies of highest weight orbits
| Autor: | Gorodentsev, A. L., Khoroshkin, A. S., Rudakov, A. N. |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Moscow Seminar on Mathematical Physics, II. :79-120 |
| ISSN: | 2472-3193 0065-9290 |
| DOI: | 10.1090/trans2/221/05 |
| Popis: | 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 Pl\"ucker embeddings of grassmannians $\Gr(2,N)$. Comment: 35 pages, some references and acknowledgments are added to the previous version |
| Databáze: | OpenAIRE |
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