Calogero-moser Pairs and the Airy and Bessel Bispectral Involutions
نویسنده
چکیده
This paper follows upon the study of the Airy bispectral involution made in [KR]. There we gave an analogue, for arbitrary rank, of the rank-one bispectral involution developed by Wilson [W1]. Recently, [W2], Wilson has established a relationship between the rank-one bispectral involution and the complex analogue of the CalogeroMoser phase space. This relationship leads to explicit formulae for the Baker function and the corresponding involution, which make many important features manifest. As shown below, similar results hold for bispectral algebras obtained from generalized Airy and Bessel operators. Given a positive integer n, define Cn to be the quotient, under conjugation by Gl(n,C), of the space of pairs (Calogero-Moser pairs) of n × n complex matrices, (P,Q), such that
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