Speaker :
| Ruibin Zhang (University of Sydney) |
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Title :
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Second fundamental theorem of invariant theory for orthogonal and symplectic groups |
Time :
| 2012-12-17 (Mon) 14:00 - 15:00 |
Place : |
Room 202, Astro-Math. Building |
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Abstract: |
The first and second fundamental theorems (FFT and SFT) of classical invariant theory are respectively concerned with generators and relations for invariants of group actions. Let G be the orthogonal group O(V) or the symplectic Sp(V), and let be the algebra of endomorphisms of . The FFT of the invariant theory of G in this setting states that there is a surjective algebra homomorphism from the Brauer algebra of degree r to the subalgebra of invariants in End(). However, the SFT remained elusive in this setting. We will develop an SFT by studying a category of Brauer tangle diagrams, and discuss the generalization of the results to the corresponding quantum groups. This is joint work with Gus Lehrer. |
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