##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Bertram Kostant

#### Massachusetts Institute of Technology

## On maximal Poisson commutative subalgebras of S(g), complete integrability, and corresponding Darboux coordinates on any reductive Lie algebra $\frak g$

##### Abstract:

Recently, using Gelfand-Zeitlin and the space of Hessenberg matrices, Wallach and I found natural Darboux coordinates (as a classical mechanical solution of the Gelfand-Zeitlin question) on $\frak g$ for the case where $\frak g$ is the space of all matrices. Now, at least locally, I do the same for any reductive $\frak g$ using a beautiful result of A. A. Tarasov on Fomenko-Miscenko theory and old results of mine on a generalization of the Hessenberg matrices.

Host: Nolan Wallach

### March 13, 2007

### 2:30 PM

### AP&M 7218

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