New York Journal of Mathematics
Volume 19 (2013) 189-251


Anthony C. Kable

On certain conformally invariant systems of differential equations

view    print

Published: June 1, 2013
Keywords: Heisenberg Laplacian, generalized Verma module, systems of differential equations on nilpotent groups
Subject: Primary 35R03; Secondary 22E25, 22E46, 22E47

Several systems of differential operators are constructed and their study is commenced. These systems are generalizations, in a reasonable sense, of the Heisenberg Laplacian operators introduced by Folland and Stein. In particular, they admit large groups of conformal symmetries; various real form of the special linear groups, even special orthogonal groups, and the exceptional group of type E6 appear in this capacity.

Author information

Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA