The center of is the set of symmetric polynomials in commuting transposition-sums

Author:
Gadi Moran

Journal:
Trans. Amer. Math. Soc. **332** (1992), 167-180

MSC:
Primary 20C30; Secondary 05E05, 05E10

DOI:
https://doi.org/10.1090/S0002-9947-1992-1062873-1

MathSciNet review:
1062873

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Abstract: Let be the symmetric group on the symbols . We show that the center of the group-ring coincides with the set of symmetric polynomials with integral coefficients in the elements , where is a sum of transpositions, . In particular, every conjugacy-class-sum of is a symmetric polynomial in .

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1062873-1

Article copyright:
© Copyright 1992
American Mathematical Society