Review of “Jack, Hall-Littlewood and Macdonald polynomials”, V. B. Kuznetsov and S. Sahi (eds.)

The book under review contains the Proceedings of a Workshop held in 2003 in Edinburgh, UK. This workshop paid attention to (in fact, celebrated) the pioneering work by the mathematicians Henry Jack, Philip Hall and D. E. Littlewood on two new families of symmetric polynomials, and to the magnificent job done by Ian Macdonald to bring these two classes of polynomials together in a more general family of symmetric polynomials. But most lectures described new developments involving these polynomials. Jack, Hall and Littlewood all lived and worked in England, Scotland or Wales, as does Macdonald, so it was very appropriate to hold this workshop in the UK. The remarkable story about the life and work of these four people fills the first 125 pages of the volume. The remaining two third of the volume is filled with 13 papers describing recent research. All authors of the research papers have earlier made important contributions to the development of the subject. I will pay most attention in this review to the first, historical part of the Volume. It contains short biographies of the four main characters, reprints of the original papers introducing the various polynomials, including an unpublished manuscript by Jack followed by comments by Macdonald. Some relevant letters are also included. It is striking to read in the biographies about the isolation of Jack, Hall and Littlewood. Jack was a Reader in Dundee, Scotland. He never ventured far from Scotland and he did not attend conferences (except for ICM, Amstrdam, 1954). Hall was the only algebrist in Cambridge. He was reticent and cared little for large gatherings. Littlewood was a full professor in Bangor, Wales. He also kept away from mathematical meetings. He never met Hall. Eventually he stopped publishing because “there is no point in writing papers of which nobody takes any notice”.