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- Title
On the structures of hive algebras and tensor product algebras for general linear groups of low rank.
- Authors
Kim, Donggyun; Kim, Sangjib; Park, Euisung
- Abstract
The tensor product algebra TA (n) for the complex general linear group GL (n) , introduced by Howe et al., describes the decomposition of tensor products of irreducible polynomial representations of GL (n). Using the hive model for the Littlewood–Richardson (LR) coefficients, we provide a finite presentation of the algebra TA (n) for n = 2 , 3 , 4 in terms of generators and relations, thereby giving a description of highest weight vectors of irreducible representations in the tensor products. We also compute the generating function of certain sums of LR coefficients.
- Subjects
TENSOR algebra; TENSOR products; LINEAR algebra; IRREDUCIBLE polynomials; LOW-rank matrices; GENERATING functions; ALGEBRA
- Publication
International Journal of Algebra & Computation, 2019, Vol 29, Issue 7, p1193
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196719500462