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Results tagged with symmetric-functions
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user 100284
Symmetric functions are symmetric polynomials, in finitely many, or countably infinitely many variables. They arise in the representation theory of symmetric groups and in the polynomial representation theory of general linear groups. Bases of the ring of symmetric functions are indexed by integer partitions. Schur functions, elementary symmetric functions, complete symmetric functions, and power sum symmetric functions are the most commonly used bases.
1
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Jack symmetric functions and their inner products
You ask what happens when you vary the parameter $\alpha$ of the inner product, but not for the Jack polynomials. I cannot say much in the general case, but one instance of interest for me was when th …
- 86
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Accepted
Normalization of Jack polynomial integral-scalar product?
Yes, my friend. Take $J_\lambda^{(\alpha)}$ in the J-normalization. Let $n$ be the number of variables (which for you is $2$). Let $\lambda'$ denote the conjugate partition to $\lambda$.
Define
$$
C_\ …
- 86