First Fundamental Theorem for Covariants of Classical Groups |
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Authors: | DA Shmelkin |
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Institution: | Independent Moscow University, Moscow, Russia |
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Abstract: | Let U(G) be a maximal unipotent subgroup of one of the classical groups G=GL(V), O(V), Sp(V). Let W be a direct sum of copies of V and its dual V*. For the natural action U(G) : W, we describe a minimal system of homogeneous generators for the algebra of U(G)-invariant regular functions on W. For G=O(V), Sp(V), this result is connected with a construction for the irreducible representations of G due to H. Weyl. |
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Keywords: | covariant syzygy partition Young symmetrizer |
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