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REPRESENTATION THEORY OF LIE GROUPS
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Representation Theory of Lie Groups is the systematic study of symmetries and ways of exploiting them. It is an extremely important discipline in modern mathematics and has strong connections with and applications to such diverse fields as number theory and mathematical physics. The famous M. Gromov eloquently puts it: "The search for symmetries and regularities in the structure of the world will always stay at the core of mathematics and physics."
The programme will focus on three sub-themes:
1. Representation of p-adic Groups - The most exciting recent progresses are the proof of the Local Langlands Conjecture and the new constructions of discrete series representations. The latter topic can be traced to the fundamental work of Roger Howe. For the Local Langlands Conjecture, the current proof involves tools from number theory and algebraic geometry and represent a new set of promising ideas that may continue to bear fruits in the near future.
2. Unitary Representation of Real Reductive Groups - One of the most fundamental problems in representation theory is to understand the unitary dual of a real reductive group. While there were remarkable progresses in the last few decades such as Harish-Chandra's work on discrete series, the mystery of the unitary dual very much remains. Topics covered in this sub theme will include the orbit method and its ramifications, for instance, understanding the unitary dual through wavefront sets and other related invariants. As much of the mystery involves singular unitary representations, the subject will also be featured prominently.
3. Multiplicity-Free Actions and Representations - Multiplicity -free actions are those group actions, which have simple spectrum. On the one hand, they are special enough to allow a deeper understanding, even permitting classifications in certain contexts. On the other hand, many interesting representations of Lie groups are often multiplicity-free as representations of other groups such as the maximal compact subgroups. In this sub theme, we will explore the intimate link between the theory of multiplicity-free actions, invariant theory and representation theory.
Tutorial and Workshop Dates
Sub-theme |
Tutorial |
Workshop |
1. |
8 - 12 Jul 2002 |
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2. |
5 - 8 Aug 2002 |
12 - 16 Aug 2002 |
3. |
6 - 10 Jan 2003 |
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* IMS Membership is not required for participation in workshops and tutorials. For attendance at workshop and/or tutorial, please complete the registration form (MSWord|PDF|PS) and fax or email to us.
The Institute for Mathematical Sciences invites applications for membership for participation in the above program. Limited funds to cover travel and living expenses are available. Applications should be received at least three (3) months before the commencement of membership.
More information is available by writing to:
Secretary
Institute for Mathematical Sciences
National University of Singapore
3 Prince George's Park Singapore 118402
Republic of Singapore
For enquiries on scientific aspects of the program, please email Eng-Chye Tan at mattanec@nus.edu.sg.
Organizers
·
Confirmed visitors
· Overview · Schedule of
talks and tutorials
Papers and
lecture notes · Membership
application
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