Celebratio Mathematica — Benkart

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G. Benkart, C. L. Shader, and A. Ram: “Tensor product representations for orthosymplectic Lie superalgebras,” J. Pure Appl. Algebra 130 : 1 (August 1998), pp. 1–48. MR 1632811 Zbl 0932.17008 ArXiv math/9607232 article

We derive a general result about commuting actions on certain objects in braided rigid monoidal categories. This enables us to define an action of the Brauer algebra on the tensor space \( V^{\otimes k} \) which commutes with the action of the orthosymplectic Lie superalgebra \( \operatorname{spo}(V) \) and the orthosymplectic Lie color algebra \( \operatorname{spo}(V,\beta) \). We use the Brauer algebra action to compute maximal vectors in \( V^{\otimes k} \) and to decompose \( V^{\otimes k} \) into a direct sum of submodules \( T^{\lambda} \). We compute the characters of the modules \( T^{\lambda} \), give a combinatorial description of these characters in terms of tableaux, and model the decomposition of \( V^{\otimes k} \) into the submodules \( T^{\lambda} \) with a Robinson–Schensted–Knuth-type insertion scheme.

Arun Ram	Related
Chanyoung Lee Shader	Related