Skew Pieri algebras of the general linear group
- Authors
- Kim, Sangjib; Lee, Soo Teck; Wang, Yi
- Issue Date
- 12월-2018
- Publisher
- AMER INST PHYSICS
- Citation
- JOURNAL OF MATHEMATICAL PHYSICS, v.59, no.12
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL PHYSICS
- Volume
- 59
- Number
- 12
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/71390
- DOI
- 10.1063/1.5050052
- ISSN
- 0022-2488
- Abstract
- Let V be an irreducible polynomial representation of the general linear group GL(n) = GL(n)(C) and let alpha(1), ... , alpha(q) be nonnegative integers less than or equal to n. We call a description of the irreducible decomposition of the tensor product V circle times Lambda(alpha 1) (C-n) circle times ... circle times Lambda(alpha q)(C-n) an iterated skew Pieri rule for GL(n). In this paper, we define a family of complex algebras whose structure encodes an iterated skew Pieri rule for GL(n), 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. Published by AIP Publishing.
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