?
Dunkl operators at infinity and Calogero-Moser systems
Sergeev A.
Translator: A. P. Veselov
Language:
English
Publication based on the results of:
A.K.Pogrebkov, Journal of Nonlinear Mathematical Physics 2020 Vol. 27 No. 2 P. 324–336
Construction of new integrable systems and methods of their investigation is one of the main directions of development of the modern mathematical physics. Here we present an approach based on the study of behavior of roots of functions of canonical variables with respect to a parameter of simultaneous shift of space variables. Dynamics of singularities ...
Added: February 21, 2020
Finkelberg M. V., Ginzburg V., Ionov A. et al., Selecta Mathematica, New Series 2016 Vol. 22 No. 4 P. 2491–2534
We study the natural Gieseker and Uhlenbeck compactifications of the rational Calogero–Moser phase space. The Gieseker compactification is smooth and provides a small resolution of the Uhlenbeck compactification. We use the resolution to compute the stalks of the IC-sheaf of the Uhlenbeck compactification. ...
Added: September 4, 2016
Finkelberg M. V., Ginzburg V., Ionov A. et al., / Series math "arxiv.org". 2015.
We study the natural Gieseker and Uhlenbeck compactifications of the rational Calogero–Moser phase space. The Gieseker compactification is smooth and provides a small resolution of the Uhlenbeck compactification. This allows computing the IC stalks of the latter. ...
Added: November 15, 2015
Sergeev A., Veselov A. P., Glasgow Mathematical Journal 2016 Vol. 58 No. 3 P. 599–616
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 ...
Added: September 4, 2015