Baker–akhiezer Function as Iterated Residue and Selberg-Type Integral

Abstract

Abstract.A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to A n -type root system in both the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a Selberg-type integral and generalise it to the deformed A n,1 -case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integrals.2002 Mathematics Subject Classification. 33E30, 81R12.

Source Identity and Kernel Functions for Elliptic Calogero–Sutherland Type Systems

“…Generalizations of the identities in [12] to the relativistic (Ruijsenaars) generalization of the CS-model [13] with a restriction on parameters as in (16) were recently given by Komori, Noumi, and Shiraishi [14]; see also [15] and references therein for related results. Identities like in (5) were also used in other works to construct eigenfunctions CS-type operators, including [14,16,17].…”

Александр Петрович Веселов (К Шестидесятилетию Со Дня Рождения)

“…Мотивируясь соответствием Мацуо-Чередника, А. П. Веселов и Дж. Фельдер нашли полный набор полиномиальных решений уравнений Книжника-Замолодчикова и формулу для функции Бейкера-Ахиезера систем Калоджеро-Мозера с целыми параметрами через итерацию взятия вычетов [57], [62]. В работе [52] Набор систем Годена естественным образом является подмногообразием в грассманиане (n − 1)-мерных плоскостей в Vn.…”

Baker-Akhiezer functions and generalised Macdonald-Mehta integrals

“…where L is the operator (8). Second, acting by L q in the variables µ and making use of the fact L q commutes with L, and then setting µ = 0, we infer from (14) and the assumption φ(0, 0) = 0 that…”