## Substitutional AnalysisThis classic monograph on representation theory and the symmetric group is suitable for advanced undergraduates and graduate students of mathematics. The Bulletin of the American Mathematical Society hailed Daniel Edwin Rutherford's treatment as "a long overdue account of Young's representation theory of the symmetric group," noting that "many of Young's complicated proofs have been simplified through a free use of mathematical induction."Starting with an elementary overview of the theory of the symmetric group, the book proceeds to an examination of Young's formula, followed by an introduction to the fundamental notion of a standard diagram. Subsequent chapters present the passage to orthogonal and natural representations. No prior knowledge of the general theory of group characters is assumed, and the author deduces the necessary theory for the symmetric group. The final chapter illustrates the substitutional aspect of the theory, and a helpful appendix and bibliography conclude the text. |

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appear arbitrary associated axial distance chapter coefficient coeﬂicient coeﬂicient of e column conclude construct cycle of order deduce deﬁne deﬁnition denote diﬁerent distorted shape equation LX equivalent evaluate fact ﬁnd ﬁrst formula group algebra group characters Hence invariant quadratic involve irreducible representations Journal of Math last equation last letter sequence leading diagonal linear combination linearly independent linearly independent solutions London Math lower node master idempotent matrix equation natural representation natural units non-singular matrix non-zero notation number of linearly obtained odd permutation order f orthogonal representation partition partitioned matrix position Proc proof prove quantitative substitutional analysis regular application relations right-hand side satisﬁed Schur semi-normal representation singular spaces standard tableaux sub-group submatrix substitutional equations substitutional expression suﬂix Suppose symmetric group tableaux of shape theorem 18 Thrall tion transpositions unit matrix upper nodes vanishes veriﬁed vertical steps write yields Young zero