The Chern Character of the Symmetric Space $\textit{El}$

Let E6 be the compact, 1 -connected, exceptional Lie group of rank 6 and PSp(4) = 5/7(4) /{±/4} the coset space of the symplectic group of degree 4 by its center (where In denotes the unit matrix of degree «). There is an involutive automorphism p:E6-*E6 whose fixed point set Eg is PSp(4) (see [9]). So the coset space E6/PSp(4) is a compact, 1 -connected, irreducible symmetric space which is denoted by El in E. Cartan's notation. The cohomology and Ktheory of El = E6/PSp(4) are known (see [3], [4] and [6]). In this paper we describe the Chern character homomorphism of El. According to Ishitoya [3], the cohomology of El is as follows. Its rational cohomology ring is given by