Jack polynomial

**Jack polynomials** (or Jack symmetric functions) form a class of symmetric functions $J_\lambda^\alpha$ labelled by a partition $\lambda$ and a parameter $\alpha$; by a result of I. G. Macdonald, they form a family of orthogonal polynomials. Jack polynomials can be defined as eigenfunctions of certain Laplac/Beltrami type operator coming in the theory of Calogero integrable systems and in random matrix theory. If $\alpha = 1$ the Jack polynomials become Schur polynomials.

- Henry Jack,
*A class of symmetric polynomials with a parameter*, Proc. Roy. Soc. Edinburgh Sec. A: Math. Phys. Sci. 69, 1-18, 1969-70, MR289462; reprinted in: Contemp. Math.**417**, Jack, Hall-Littlewood and Macdonald polynomials, 57–74, Amer. Math. Soc. 2006 - H. Jack,
*A class of polynomials in search of a definition, or the symmetric group parametrized*, in: Jack, Hall-Littlewood and Macdonald polynomials, 75–106, AMS 2006 - Wolframwolrd: Jack polynomial
- I. G. Macdonald,
*Symmetric functions and Hall polynomials*, Oxford Math. Monographs, 2nd enlarged ed. 1995 - Richard P. Stanley,
*Some combinatorial properties of Jack symmetric functions*, Adv. Math.**77**(1989), no. 1, 76–115, MR90g:05020 doi

Created on October 11, 2011 22:04:37
by Zoran Škoda
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