Seminar Algebra and Geometry: Tommy Wuxing Cai (Universität Basel)

Vertex operator realizations of Jack symmetric functions

We first realize Jack function of rectangular shapes. Then we introduce an iterative method to realize Jack functions of general shapes from those of rectangular shapes. As a byproduct, we prove some special cases of Richard P. Stanley's conjecture about the positivity of the Littlewood-Richardson coefficients of Jack functions.

Contents:
1. partitions and symmetric functions
2. Some history and questions about symmetric functions
3. Vertex operator realization of rectangular Jack functions
4. A special case of Stanley's conjecture and the realization of general Jack functions
5. Open questions

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