• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site

## Jack-Laurent symmetric functions for special values of parameters

Glasgow Mathematical Journal. 2016. Vol. 58. No. 3. P. 599-616.
Sergeev A., Veselov A.

We consider the Jack–Laurent symmetric functions for special values of parameters p0=n+k−1m, where k is not rational and m and n are natural numbers. In general, the coefficients of such functions may have poles at these values of p0. The action of the corresponding algebra of quantum Calogero–Moser integrals $\mathcal{D}$(k, p0) on the space of Laurent symmetric functions defines the decomposition into generalised eigenspaces. We construct a basis in each generalised eigenspace as certain linear combinations of the Jack–Laurent symmetric functions, which are regular at p0=n+k−1m, and describe the action of $\mathcal{D}$(k, p0) in these eigenspaces.