Differential Operators , Shifted Parts , and Hook Lengths

  title={Differential Operators , Shifted Parts , and Hook Lengths},
  author={Tewodros Amdeberhan},
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