Determinantal Expression and Recursion for Jack Polynomials

Luc Lapointe, A. Lascoux, J. Morse
1999 Electronic Journal of Combinatorics  
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
more » ... A specialization of these results yields a determinantal formula for the Schur functions and a recursion for the Kostka numbers.
doi:10.37236/1539 fatcat:nonzpotxinhblpinexqp3qdygi