I guess this is an old thread now, but I always thought that James' proof was a little indirect and not very explicit. A much nicer proof was given by Steen Ryom-Hansen in his paper “Grading the translation functors in type A.” Journal of Algebra 274, no. 1 (2004): 138–63; see arXiv:0301.5285.

To blow my own trumpet, a "cellular algebra" proof in the cyclotomic case (which includes the symmetric groups) is given in arXiv:0903.4493. For the corresponding result in the graded setting, following Ryom-Hansen, see arXiv:1008.1462.

All of these arguments work over arbitrary rings.

I guess this is an old thread now, but I always thought that James' proof was a little indirect and not very explicit. A much nicer proof was given by Steen Ryom-Hansen in his paper “Grading the translation functors in type A.” Journal of Algebra 274, no. 1 (2004): 138–63; see arXiv:math/0301285.

To blow my own trumpet, a "cellular algebra" proof in the cyclotomic case (which includes the symmetric groups) is given in arXiv:0903.4493. For the corresponding result in the graded setting, following Ryom-Hansen, see arXiv:1008.1462.

All of these arguments work over arbitrary rings.

I guess this is an old thread now, but I always thought that James' proof was a little indirect and not very explicit. A much nicer proof was given by Steen Ryom-Hansen in his paper “Grading the translation functors in type A.” Journal of Algebra 274, no. 1 (2004): 138–63; see arXiv:0301.5285.

To blow my own trumpet, a "cellular algebra" proof in the cyclotomic case (which includes the symmetric groups) is given in arXiv:0903.4493. For the corresponding result in the graded setting, following Ryom-Hansen, see arXiv:1008.1462.

All of these arguments work over arbitrary rings.

I guess this is an old thread now, but I always thought that James' proof was a little indirect and not very explicit. A much nicer proof was given by Steen Ryom-Hansen in his paper “Grading the translation functors in type A.” Journal of Algebra 274, no. 1 (2004): 138–63; see arXiv:0301.5285.

To blow my own trumpet, a "cellular algebra" proof in the cyclotomic case (which includes the symmetric groups) is given in arXiv:0903.4493. For the corresponding result in the graded setting, following Ryom-Hansen, see arXiv:1008.1462.

All of these arguments work over arbitrary rings.