Sophus Lie
Sophus Lie

Richard Askey
Richard Askey

Ian Macdonald
Ian Macdonald

Course on Special functions and Lie theory (February-May 2008)

This is a course aimed at master students in mathematics and mathematical physics.

General information

Lecturer:   Tom H. Koornwinder

Time and place: Thursday, 14.00-16.45 hour, room I.101, Nieuwe Achtergracht 170, Amsterdam.
The first session is on February 7, the last session on May 29. There will be no session on March 27, May 1 and May 22.

Credits: 6 EC


Roughly, the course consists of the following three parts: Further details will be provided at the beginning of the course, also depending on preferences and earlier knowledge of participants.

Form of teaching

On the basis of partial lecture notes to be provided by the lecturer, parts of books, and journal articles, theory will be explained. Possibly, during the third hour, exercises may be treated and students may give presentations.


A combination of submitted exercises (one exercise for each session), student presentations (one by each student), and a final paper.

Preliminary literature

Some preliminary knowledge about the relationship between a Lie group and a Lie algebra is helpful, but not strictly necessary. General abstract concepts will be explained for special examples. For introductory reading I recommend: For introductory reading on special functions and orthogonal polynomials I recommend:

Lecture notes and exercises

Lecture notes on the first part (SU(2) and spherical harmonics) were made available as downloadable pdf each week. These can now be downloaded together in one file: SFLie.pdf.

week file exercises
1 (7 Feb) SFLie1.pdf 1.13 (p.5), 1.15 (p.11)
2 (14 Feb) SFLie2.pdf 1.26 (p.21), 1.27 (p.22)
3 (21 Feb) SFLie3.pdf 1.37 (p.31), 1.38 (p.31)
4 (28 Feb) SFLie4.pdf 2.3 (p.38), 2.4 (p.38)
5 (6 Mar) SFLie5.pdf 2.15 (p.45), 2.16 (p.46)
6 (13 Mar) SFLie6.pdf 2.22, 2.23, 2.24 (p.51)
7 (20 Mar) SFLie7.pdf 2.30. 2.31 (p.57)
8 (3 Apr) SFLie8a.pdf, SFLie8b.pdf 2.39, 2.40 (p.62)
9 (10 Apr)
10 (17 Apr) exercisesWeek10.pdf
(last modified 28 July)
1, 2
11 (24 Apr) exercisesWeek11.pdf 1, 2
12 (8 May)
13 (15 May)
14 (29 May)

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