Mathematical Sciences: Analysis on Nilpotent Lie groups
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Lie groups arise naturally in mathematics and physics as                    groups of symmetries.  An interesting example that lies readily                 at hand consists of all rotations of a sphere, made into a group                by applying rotations successively.  The simplest noncommutative                example of a nilpotent Lie group is the Heisenberg group of upper               triangular three-by-three real matrices with ones on the                        diagonal.  The Heisenberg group plays a fundamental role in the                 quantum mechanical treatment of the harmonic oscillator.                             Nilpotent Lie groups are sufficiently well understood that                 one can do analysis on them in almost the same level of detail as               Fourier analysis in the classical, Euclidean setting.  The                      project of Professor Jenkins has two main objectives.  The first                and more important goal is to classify Gelfand pairs (roughly, a                Lie group together with a compact subgroup of automorphisms                     satisfying a certain commutativity condition) in the nilpotent                  case.  The second is to find out more about the space of                        spherical functions relative to such a pair.
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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