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Abstract
© 2018 Author(s). Let V be an irreducible polynomial representation of the general linear group GLn=GLn(C) and let α1, ⋯, αq be nonnegative integers less than or equal to n. We call a description of the irreducible decomposition of the tensor product V⊕ - Λα1(Cn) ⊕ - Λαq(Cn) an iterated skew Pieri rule for GLn. In this paper, we define a family of complex algebras whose structure encodes an iterated skew Pieri rule for GLn, and we call these algebras iterated skew Pieri algebras. Our main goal is to construct a basis for each of these algebras thereby giving explicit highest weight vectors in the above tensor product.
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Source Title
Journal of Mathematical Physics
Publisher
AIP Publishing
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Date
2018-12-01
DOI
10.1063/1.5050052
Type
Article