Geodesic
Higher-Dimensional Representations of the Reflection Equation Algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 45-61

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We consider a new method for constructing finite-dimensional irreducible representations of the reflection equation algebra. We construct a series of irreducible representations parameterized by Young diagrams. We calculate the spectra of central elements $s_k=\operatorname{Tr}_qL^k$ of the reflection equation algebra on $q$-symmetric and $q$-antisymmetric representations. We propose a rule for decomposing the tensor product of representations into irreducible representations.
Keywords: reflection equation algebra, Hecke algebra, representations. 
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     author = {D. I. Gurevich and P. A. Saponov},
     title = {Higher-Dimensional {Representations} of the {Reflection} {Equation} {Algebra}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a3/}
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D. I. Gurevich; P. A. Saponov. Higher-Dimensional Representations of the Reflection Equation Algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 45-61. http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a3/