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| HAL: hal-00330641, version 1 |
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| Advances in Mathematics 201, 2 (2006) 379-407 |
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| A universal dimension formula for complex simple Lie algebras |
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| Joseph M. Landsberg 1Laurent Manivel 2 |
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| (2006-04-15) |
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| We present a universal formula for the dimension of the Cartan powers of the adjoint representation of a complex simple Lie algebra (i.e., a universal formula for the Hilbert functions of homogeneous complex contact manifolds), as well as several other universal formulas. These formulas generalize formulas of Vogel and Deligne and are given in terms of rational functions where both the numerator and denominator decompose into products of linear factors with integer coefficients. We also discuss some consequences of the formulas including a relation with Scorza varieties. |
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| 1: | Department of Mathematics, Texas A&M University (TAMU) |
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Météo France |
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| 2: | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| Subject | : | Mathematics/Algebraic Geometry |
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| simple Lie algebra – adjoint representation – Hilbert function – Scorza variety |
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| Attached file list to this document: | ||||||||||
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| hal-00330641, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00330641 | |
| oai:hal.archives-ouvertes.fr:hal-00330641 | |
| From: Laurent Manivel | |
| Submitted on: Wednesday, 15 October 2008 10:48:43 | |
| Updated on: Wednesday, 15 October 2008 11:51:10 | |
