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First Fundamental Theorem for Covariants of Classical Groups

✍ Scribed by D.A. Shmelkin

Book ID
102564471
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
365 KB
Volume
167
Category
Article
ISSN
0001-8708

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✦ Synopsis

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 g . 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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This paper gives a partial answer to the Cherlin᎐Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main res