GROUP REPRESENTATIONS and FUNCTIONAL ANALYSIS

M393c     # 52265   FALL, 1996  Tues-Thurs 11:00-12:30

Instructor: Charles Radin

This course has two objectives: to give an introduction to
representation theory and to functional analysis. More specifically,
we will be developing basic parts of functional analysis with the goal
of using them in the representation of groups.

The representation of groups breaks naturally into a few classes. The
finite groups, abelian groups, and compact groups have a rather
satisfactory theory which we will analyze (symmetric groups, character
theory, the rotation group S(O,3), the Peter-Weyl theorem). But it
is with the nonabelian, noncompact groups (Heisenberg group,
SL(2,\R)) and their infinite dimensional irreducible representations
(for which representation theory is much less complete) where we will
really see the power of functional analysis. We will not delve into
general Lie theory.

The only prerequisite is graduate standing; an attempt will be made to
accommodate a diversity of backgrounds.

Prerequisites: as noted above

Textbook: none required (though several will be put on reserve in the 
library).

Consent of Instructor: not required

For more information: Charles Radin
RLM 12.114
471-0174