Susana Salamanca's  Home Page

Areas of Interest: Representation Theory of Real Lie groups and Lie algebras and related areas

Research Topics: My research focuses on the study of the unitary representations of real reductive Lie groups. This subject has applications to number theory, automorphic forms, class field theory, mathematical physics, control theory and many other areas of research. The field intertwines ideas of harmonic analysis, algebra, geometry and topology.

I study these representations via the equivalent problem of classifying the unitarizable Harish Chandra modules of G.  these are representations of both, the Lie algebra of G and of a maximally compact subgroup K of G.
My current research includes a program proposed in collaboration with David Vogan to reduce the classification of the unitary dual to a smaller set of representations and a program proposed by and in collaboration with Dan Barbasch and David Vogan and Jeff Adams to generalize Barbasch's classification of the Spherical unitary dual for Split real and p-adic groups.

Recently I have become involved in the Atlas of Lie groups and Representations project (see http://www.math.umd.edu/~jda/atlas/) This is a project, in collaboration with several colleagues, to make available information about representations of non-compact semi-simple Lie groups (and related groups over local fields). One of the goals of the Atlas is to put together such a data base for groups like SL(n, R ) or Sp(2n, R), that will be available for use in other fields of research like automorphic forms, class field theory, etc.

The people involved in this project now are Jeffrey Adams, Dan Barbasch, Dan Ciubotaru, Fokko du Cloux, Anthony Knapp, Annegret Paul, Siddharta Sahi, John Stembridge, Peter Trapa, Marc van Leeuwen, David Vogan, Jiu-Kang Yu and myself.
 



 

Teaching: For general information about the Mathematical Sciences Department courses please see NMSU Math Department

Courses: For information, syllabi, etc on the following courses click on the links below

Fall 2007

  1. Math 481/525 Section 1. Meets TR 10:20-11:35

Fall 2006

  1. Math 471 Section 1.  Meets MWF 10:30 to 11:20 AM in Room SH109


Please send mail to ssalaman@nmsu.edu if you have any comments.