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Results tagged with symmetric-polynomials
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user 11260
7
votes
Accepted
The coefficients of the Jack polynomials are polynomials in the Jack parameter
Following up on the suggestion of LSpice, to remove this from the "unanswered queue":
the combinatorial formula in Wikipedia, due to Knop and Sahi, is a polynomial in $\alpha$.
- 188k
4
votes
Accepted
Eigenvalues of the Jack polynomials for the Calogero-Sutherland operator
There may an issue here with different definitions of the CS operator. The second expression for the eigenvalues in the OP is for a slightly different operator:
\begin{align}
&H=\frac{\alpha}{2}\sum_{ …
- 188k
11
votes
Formula expressing symmetric polynomials of eigenvalues as sum of determinants
Concerning the reference request:
Several text books [1,2] give the theorem and proof for elementary symmetric polynomials $s_k=$ sum of all $k\times k$ principal minors of the $n\times n$ matrix. Thi …
- 188k