The inverse Abel transform for an exceptional bounded symmetric domain (Q1373844)

The exceptional bounded symmetric domain \(E_6/ \text{spin} (10)\times T\) is a noncompact Hermitian symmetric space of rank 2; its Lie algebra has the structure of a \(bc_2\) root system. By using the first shift operator of this system four times, the elementary spherical functions on the domain are transformed into those on a complex hyperbolic space. The inverse Abel transform for this space is obtained by analyzing the Harish-Chandra \(C\)-function. As a consequence, an expression of the heat kernel is derived.