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Zonal polynomials and domino tableaux. (English) Zbl 0759.05098
Let $$H$$ be a subgroup of a finite group $$G$$. One can define the idempotent element $$\theta$$ of the group algebra $${\mathcal A}(G)$$ by $$\theta=\Sigma_{h\in H}h/| H|$$. If $$(H,G)$$ is a Gelfand pair then the decomposition of $$\theta$$ into minimal idempotents yields a basis for the Hecke algebra $${\mathcal H}(H,G)$$. The authors prove that the Fourier transform of the minimal idempotents is supported by standard domino tableaux. Moreover, they present a multiplication algorithm for zonal polynomials and relate the expansion coefficients to the Littlewood-Richardson’s coefficients.
Reviewer: J.Vinárek (Praha)

##### MSC:
 5e+10 Combinatorial aspects of representation theory 500000 Symmetric functions and generalizations
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##### References:
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