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| Article Detail Infomation |
| Title : |
| The Eigencone and Saturation for Spin(8) |
| Issue Number : |
Volume 5, Number 2, 2009 (Friedrich Hirzebruch special issue, part I) |
| Author : |
Michael Kapovich, Shrawan Kumar and John J. Millson |
| Description : |
| We explicitly calculate the system of restricted triangle inequalities for the group PSO(8) given by Belkale-Kumar, thereby explicitly solving the eigenvalues of a sum problem for this group (equivalently describing the side-lengths of geodesic triangles in the corresponding symmetric space for the metric d¢ with values in the Weyl chamber ¢). We then apply some computer programs to verify the saturation conjecture for the decomposition of tensor products of ¯nite-dimensional irreducible representations of Spin(8). Namely, we show that for any triple of dominant weights (¸; ¹; º) such that ¸ + ¹ + º is in the root lattice, and any positive integer N, |
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