We compute the heat kernel on the classical and nonisotropic Heisenberg groups, and on the free step two nilpotent groups , by an elementary method, in particular without using Laguerre calculus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-9, author = {Fran\c coise Lust-Piquard}, title = {A simple-minded computation of heat kernels on Heisenberg groups}, journal = {Colloquium Mathematicae}, volume = {96}, year = {2003}, pages = {233-249}, zbl = {1052.43013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-9} }
Françoise Lust-Piquard. A simple-minded computation of heat kernels on Heisenberg groups. Colloquium Mathematicae, Tome 96 (2003) pp. 233-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-9/