Bases for some reciprocity algebras I

Abstract

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 (C) x GL m1 (C) x GL m2 (C) x ... x GL mr (C) highest weight vectors in P (C n ⊗ C m ), where m = m 1 +... + m r and mj < n for all 1 < j < r, and the algebra of GL n (C) x GL k (C) x GL 1 (C) highest weight vectors in P [(C n ⊗ C k ) ⊕ (C n * ⊗ C l )].