MA6012: Harmonic Analysis on Compact Lie Groups

Course Details
1. Double cover of SO(n). (3 Lecture hours)
2. Computation of Haar measure on some simple matrix groups. (2 Lecture hours)
3. Recalling Peter-Weyl Theory for compact groups. (2 Lecture hours)
4. Computation of unitary dual of SU(2) and SO(3). (3 Lecture hours)
5. Laplace operator on SU(2). (2 Lecture hours)
6. Heat equation on SU(2) and SO(2). (2 Lecture hours)
7. Spherical harmonics (4 Lecture hours)
8. Dirichlet problem and Poisson kernel (3 Lecture hours)
9. Radial part of the Laplace operator (3 Lecture hours)
10. Heat equation and orbital integrals (3 Lecture hours)

11. Analysis on space of symmetric and hermitian matrices (3 Lecture hours)
12. Highest Weight theorem (3 Lecture hours)
13. Weyl integration and character formula (3 Lecture hours)
14. Holomorphic representations (3 Lecture hours)
15. Unitary dual of U(n). (3 Lecture hours)

Text Books: (Include ISBN Numbers)
1. J. Faraut:Analysis on Lie groups Cambridge studies in advanced Mathematics 110.
2008-ISBN-13:978-0-521-71930-8

References:
1. L. Clerc, Les repr ́esentatios des groupes compacts, Analyse harmonique (J.L.Clerc
et al., ed.), C.I.M.P.A., 1982.
2. Knapp.A, Lie groups beyond introduction, 140, Birkauser, 2002, ISBN-13: 978-1-4757-
2453-0.
3. M.R. Sepanski, Compact lie groups, Springer, 2007, ISBN-13: 978-0-387-30263-8.
4. B. Simon, Representations of finite and compact Lie groups, American Mathematical
Society, 1996, ISBN-13: 978-0-8218-0453-7.
5. Zelobenko.D, Compact lie groups & their representations, ams series ed., 10, Springer,
1973, ISBN-13: 0-8218-1590-3.