##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Dusty Grundmeier

#### University of Illinois at Urbana-Champaign

## Group-Invariant CR Mappings

##### Abstract:

\indent We consider group-invariant CR mappings from spheres to hyperquadrics. Given a finite subgroup $\Gamma \subset U(n)$, a construction of D'Angelo and Lichtblau yields a target hyperquadric $Q(\Gamma)$ and a canonical map $h_{\Gamma} : S^{2n-1}/\Gamma \to Q(\Gamma)$. For every $\Gamma \subset SU(2)$, we determine this hyperquadric $Q(\Gamma)$, that is, the numbers of positive and negative eigenvalues in its defining equation. For families of cyclic and dihedral subgroups of $U(2)$, we study these numbers asymptotically as the order of group tends to infinity. Finally, we explore connections with invariant theory and representation theory.

Host: Jiri Lebl

### January 25, 2011

### 9:30 AM

### AP&M 7321

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