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The dual Cauchy identity for Jack polynomials also exists, and is better expressed in terms of the $P$-normalized Jack polynomials: $$ \sum_{\lambda} P^{(a)}_ \lambda(\underline x)P^{(1/a)} _ {\lambda'...

I'm afraid that this question has a disappointingly simple answer. Yes, the values of the Iwahori-spherical Whittaker functions have an interpretation as characters of representations; but they are ...

Yes. Here is the strategy that I typically use to derive symmetric-functions identities from symmetric-polynomials identities. It might not be the most general strategy, but it has so far been ...

Here is one possible approach to make the aruement rigorous: Define the two series on the left and the right as Taylor series over the monomials $$ y_1^{e_1} \cdot ... \cdot y_n^{e_n}; $$ in ...