Fusion products and symmetric functions

Ghislain Fourier (University of Glasgow)

Wednesday 20th November, 2013 16:00-17:00 Maths 204


Fusion products for current algebras have been introduced fifteen years ago. Roughly speaking, they make use of the natural grading of the polynomial ring to form graded tensor products of simple modules for a simple complex Lie algebra. These fusion products play a crucial role in the study of finite-dimensional modules for current or loop algebras, for instance they recover Weyl modules and Demazure modules to name but a few. Although intensively studied, various fundamental questions are not answered yet, for example about defining relations or graded character formulas.

The current state of art and as well as the strong connection to conjectures about Schur positivity of symmetric functions (and recent results here) will be presented.

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