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According to Macdonald's book, when the Jack parameter $\alpha$ is $0$,then the Jack $P$-polynomial $P_\lambda(\alpha)$ is the elementary symmetric polynomial $e_{\lambda'}$ where $\lambda'$ is the ...

Let's say that a Schur polynomial is degenerate if its number of variables is less than the weight of the partition it is associated to. For example, according to Sage, the Schur polynomial of the ...

The Calogero-Sutherland operator on the space of homogeneous symmetric polynomials in $n$ variables is defined by $$ \frac{\alpha}{2}\sum_{i=1}^n x_i^2\frac{\partial^2}{\partial x_i^2} + \frac{1}{2}\...

I developed four libraries (Julia, R, Python, Haskell) for the computation of Jack polynomials. I developed them for fun because I found this was programmatically interesting. But now I'd like them to ...

Cross posting from MSE. Definition: For any natural number $n\ge 3$, define the polynomial $P_{n}\left(x_1,x_2,...,x_{n-1},x_{n} \right)$, with indeterminates $x_{i}$, where $i\in\{1,2,...,n-1,n\}$, ...