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# Differential Operators , Shifted Parts , and Hook Lengths

@inproceedings{Amdeberhan2008DifferentialO, title={Differential Operators , Shifted Parts , and Hook Lengths}, author={Tewodros Amdeberhan}, year={2008} }

- Published 2008

We discuss Sekiguchi-type differential operators, their eigenvalues, and a generalization of Andrews-Goulden-Jackson formula. These will be applied to extract explicit formulae involving shifted partitions and hook lengths. 1. Differential operators. The standard Jack symmetric polynomials Pλ(y1, . . . , yn;α) (see Macdoland, Stanley [5, 10]) as well as their shifted counter-parts (replace θ = 1/α; see Okounkov-Olshanski [7] and references therein) have been studied. The former appear as… CONTINUE READING