Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On syzygies of highest weight orbits   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
$\Gr(2,N)$.

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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph