Pieri and Littlewood-Richardson rules for two rows and cluster algebra structure
- Authors
- Kim, Sangjib; Yoo, Semin
- Issue Date
- 5월-2017
- Publisher
- SPRINGER
- Keywords
- Cluster algebra; Highest weight vectors; Tensor product decomposition; Pieri rules; Littlewood-Richardson rules; Branching rules
- Citation
- JOURNAL OF ALGEBRAIC COMBINATORICS, v.45, no.3, pp.887 - 909
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF ALGEBRAIC COMBINATORICS
- Volume
- 45
- Number
- 3
- Start Page
- 887
- End Page
- 909
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/83563
- DOI
- 10.1007/s10801-016-0728-0
- ISSN
- 0925-9899
- Abstract
- We study an algebra encoding a twice-iterated Pieri rule for the representations of the general linear group and prove that it has the structure of a cluster algebra. We also show that its cluster variables invariant under a unipotent subgroup generate the highest weight vectors of irreducible representations occurring in the decomposition of the tensor product of two irreducible representations of the general linear group one of whom is labeled by a Young diagram with less than or equal to two rows.
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