Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0743.05072
Stanley, Richard P.
Some combinatorial properties of Jack symmetric functions. (English)
[J] Adv. Math. 77, No.1, 76-115 (1989). ISSN 0001-8708

Jack functions are symmetric functions parametrized by an indeterminate $\alpha$, which generalize Schur functions $(\alpha=1)$ and zonal polynomials $(\alpha=2)$. This paper, in the spirit of I. G. Macdonald's book {\it Symmetric functions and Hall polynomials} [Clarendon Press, New York (1979; Zbl 0487.20007)], extends many of the basic results on Schur functions to Jack functions. Induced in the paper are results due to Macdonald which appear in the second edition of the above book. The results include a definition of a parametrized hook length, evaluations of the norm of a Jack function in terms of these hook lengths, and duality results relating conjugate shapes with the reciprocal of the parameter. Several conjectures are mentioned. Among these are a conjecture that the (normalized) Kostka number analogue is a polynomial with nonnegative integer coefficients and a conjecture that the Littlewood-Richardson coefficient analogue is a polynomial with nonnegative integer coefficients.

MSC 2000:: *05E05 Symmetric functions
20C30 Representations of finite symmetric groups
05A15 Combinatorial enumeration problems

Keywords: Jack functions; Schur functions; parametrized hook length; Kostka number; Littlewood-Richardson coefficient

Citations: Zbl 0487.20007

Cited in: Zbl 0959.05116 Zbl 0760.05089

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]