The Grushin plane is a right quotient of the Heisenberg group. Heisenberg geodesics’ projections are solutions of an isoperimetric problem in the Grushin plane.

The membrane instanton superpotential for M-theory on the G 2 holonomy manifold given by the cone on S 3 × S 3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dil...

The Segal–Shale–Weil representation associates to a symplectic transformation of the Heisenberg group an intertwining operator, called metaplectic operator. We develop an explicit construction of metaplectic operators for the Heisenberg group H(G) of a finite abelian group G, an important setting in finite time-frequency analysis. Our approach also yields a simple construction for the multivari...

In an interesting note, E.M. Stein observed some 20 years ago that while the Kohn Laplacian b on functions is neither locally solvable nor (analytic) hypoelliptic, the addition of a non-zero complex constant reversed these conclusions at least on the Heisenberg group, and Kwon reproved and generalized this result using the method of concatenations. Recently Hanges and Cordaro have studied this ...