醉月湖講座
主講者: Ruibin Zhang (University of Sydney)
講題: Second fundamental theorem of invariant theory for orthogonal and symplectic groups
時間: 2012-12-17 (Mon.)  14:00 - 15:00
地點: 天文數學館2樓202教室
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 $\text{End}(V^{\otimes r})$ be the algebra of endomorphisms of $V \otimes ^{r}$ . 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($V \otimes ^{r}$). 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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