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Relative symmetric polynomials. (English) Zbl 1194.05162
Summary: We introduce the notion of a relative symmetric polynomial with respect to a permutation group and an irreducible character and we give answers for some natural questions about their structures. In order to study symmetric polynomials with respect to linear characters, we define the concept of relative Vandermonde polynomial. Finally, we present some interesting research problems concerning relative symmetric polynomials.

MSC:
05E05 Symmetric functions and generalizations
15A69 Multilinear algebra, tensor calculus
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