Find # of Independent Components of Riemann Curvature in D Dimensions

[dextercioby]

How do i find the number of independent components of the Riemann curvature tensor in D space-time dimensions.

One is given that the Riemann tensor is an (2,2) irreducible rep of GL(4, \mathbb{R}) and obeys Bianchi I

R_{[\mu\nu|\rho]\lambda}=0

Been trying this problem for 3 days and couldn't come up with a reasonable answer.


Daniel.

 

[BerkMath]

(1/12)*n^2*(n^2-1) where n=D.

 

[dextercioby]

Tx, but i found it solved in Nakahara pages 231-232.

Daniel.