Heisenberg Group Action on Quintics
This Demonstration shows the action of the Heisenberg group on a family of quintic polynomials with compact support. The Heisenberg group is a nilpotent Lie group that has a natural action on the vector space of square integrable functions on the real line. In representation theory and quantum mechanics such actions belong to the Schrödinger representation. Let be the Heisenberg group and . Schrödinger representations of type are in one-to-one correspondence with a family of linear functionals of the Lie algebra of parametrized by , where . If is square-integrable, . Such actions are simply a combination of modulations and translations.
For more information on the Heisenberg group, see http://en.wikipedia.org/wiki/Heisenberg_group.