Bases for some reciprocity algebras I
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For a complex vector space V, let P(V ) be the algebra of polynomial functions on V . In this paper, we construct bases for the algebra of all GL n () GL m1 () GL m2 () GL mr () highest weight vectors in P ( n m ), where m = m 1 + + m r and m j n for all 1 j r, and the algebra of GL n () GL k () GL 1 () highest weight vectors in P [ n k ) n* l)]. 2007 American Mathematical Society.