Course on Special functions and Lie theory
(February-May 2008)
This is a course aimed at master students in mathematics and
mathematical physics.
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:
-
Special Lie groups, their representations and related special functions.
We will start with SU(2).
-
Special quantum groups, their representations and related q-special functions
-
Macdonald polynomials and affine Hecke algebras
Further details will be provided at the beginning of the course, also
depending on preferences and earlier knowledge of participants.
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.
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:
-
A. Baker,
Matrix groups. An introduction to Lie group theory,
Springer-Verlag, 2002;
ISBN 1-85233-470-3, MR1869885.
-
B.C. Hall,
Lie groups, Lie algebras, and representations. An elementary
introduction,
Springer-Verlag, 2003;
ISBN 0-387-40122-9, MR1997306.
-
W. Rossmann,
Lie groups. An introduction through linear groups,
Oxford University Press, 2002;
ISBN 0-19-859683-9, MR1889121.
For introductory reading on special functions and orthogonal polynomials
I recommend:
-
G.E. Andrews, R. Askey and R. Roy,
Special functions,
Cambridge University Press, 1999;
ISBN 0-521-62321-9, MR1688958.
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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