Long story short, I personally find Macdonald's celebrated book Symmetric Functions and Hall Polynomials somewhat difficult to read for various reasons. I also know for a fact that I'm not the only one to hold that opinion =)

On the other hand, Macdonald polynomials have been extremely popular objects of study for quite some time now. Nonetheless, an expert in the field told me recently that he does not know of any other books that can be used as an alternative introduction to the subject. So here are my two questions.

1) What is your favorite introductory text on Macdonald polynomials, whether in the form of a book or anything else?

2) Are there any other books that focus on Macdonald's ring of symmetric functions, its generalizations and various bases therein? How do they compare to SFHP?

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    $\begingroup$ Oh, you are that Igor! I read your paper on Hall-Littlewood polynomials from Brions formula. It's quite nice! Anyway, have you had a look at Jim's book on qt-Catalan numbers? math.upenn.edu/~jhaglund It has a chapter in the end about Macdonald polynomials. $\endgroup$ Sep 6, 2015 at 17:29
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    $\begingroup$ I sympathize. I was given the book as an undergraduate and I was like "wtf?" So I did Schubert calculus instead. $\endgroup$ Sep 6, 2015 at 17:37
  • $\begingroup$ I can only say that the 2nd edition of SFHP is more readable, so if you tried the 1st one (the one translated into Russian) then you might find the 2nd one nicer. $\endgroup$ Sep 6, 2015 at 18:06
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    $\begingroup$ @PerAlexandersson Hi! Thanks for taking interest in my work and my MO questions! No, I haven't come across Haglund's book before, will certainly have a look. $\endgroup$
    – imakhlin
    Sep 6, 2015 at 18:54
  • $\begingroup$ @DimaPasechnik I've read through fair portions of both Zelevinsky's translation and Oxford's second edition. I must say I haven't felt much of a difference. I guess my problems with the text run deeper than what might change from one edition to the next. In a sense, it gives the feeling that what I'm reading is much closer to a research article than to a textbook. (This, of course, is for the specific reason of much of the material being Macdonald's original results.) $\endgroup$
    – imakhlin
    Sep 6, 2015 at 19:08

1 Answer 1


I recommend reading Macdonald's volume University Lecture Series Vol 12 Symmetric functions and orthogonal polynomials.

It is a rather short introduction to Macdonald polynomials for the symmetric group and for general finite Weyl groups, but everything is very well explained, organized, and self-contained. After reading this, I found myself much more comfortable getting back to Symmetric functions and Hall polynomials for futher background and details.


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