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Bases for some reciprocity algebras I

Bases for some reciprocity algebras I

For a complex vector space $V$, let $\mathcal {P}(V)$ be the algebra of polynomial functions on $V$. In this paper, we construct bases for the algebra of all $\operatorname {GL}_n(\mathbb {C})\times \operatorname {GL}_{m_1} (\mathbb {C})\times \operatorname {GL}_{m_2} (\mathbb {C})\times \cdot \cdot \cdot \times \operatorname {GL}_{m_r}(\mathbb {C})$ highest weight vectors in …