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Title: Skew Pieri algebras of the general linear group
Authors: Kim, S
Lee Soo Teck 
Wang, Y
Issue Date: 1-Dec-2018
Publisher: AIP Publishing
Citation: Kim, S, Lee Soo Teck, Wang, Y (2018-12-01). Skew Pieri algebras of the general linear group. Journal of Mathematical Physics 59 (12) : 121702-121702. ScholarBank@NUS Repository.
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.
Source Title: Journal of Mathematical Physics
ISSN: 0022-2488
DOI: 10.1063/1.5050052
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