Determinantal expression and recursion for Jack polynomials
The electronic journal of combinatorics, Tome 7 (2000)
We describe matrices whose determinants are the Jack polynomials expanded in terms of the monomial basis. The top row of such a matrix is a list of monomial functions, the entries of the sub-diagonal are of the form $-(r\alpha+s)$, with $r$ and $s \in {\bf N^+}$, the entries above the sub-diagonal are non-negative integers, and below all entries are 0. The quasi-triangular nature of these matrices gives a recursion for the Jack polynomials allowing for efficient computation. A specialization of these results yields a determinantal formula for the Schur functions and a recursion for the Kostka numbers.
DOI :
10.37236/1539
Classification :
05E05
Mots-clés : symmetric functions, Schur functions, Jack polynomials, Kostka numbers
Mots-clés : symmetric functions, Schur functions, Jack polynomials, Kostka numbers
@article{10_37236_1539,
author = {Luc Lapointe and A. Lascoux and J. Morse},
title = {Determinantal expression and recursion for {Jack} polynomials},
journal = {The electronic journal of combinatorics},
year = {2000},
volume = {7},
doi = {10.37236/1539},
zbl = {0934.05123},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1539/}
}
Luc Lapointe; A. Lascoux; J. Morse. Determinantal expression and recursion for Jack polynomials. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1539
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