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Issai Schur, in his doctoral thesis (1901) introduced the Schur algebra tostudy the polynomial representation theory of the general linear group. Hedescribed a basis of this algebra and structure constants. Later, Miguel Mendez(2001) gave a graph-theoretic description of Schur's basis and computed thestructure constants. In this presentation, we will give a new graphicinterpretation of the basis of Schur algebra and use it to give a descriptionof the structure constants which is equivalent to the one given by Mendez.

Graphic Interpretation of the Structure Constants of the Schur Algebra