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### Macdonald polynomials as a sum of affine Demazure characters

**Student-Run Research Seminar**

Speaker: | Lisa Johnston, UC Davis |

Location: | 2112 MSB |

Start time: | Wed, Oct 9 2024, 12:10PM |

It is known that in type $A_{n}^{(1)}$ and simply-laced types, the specialized Macdonald polynomials at $t=0$ is an affine Demazure character. In type $C_{n}^{(1)}$, there is no explicit formula describing this relationship. We begin by providing the necessary background and summarize known results in type $A_{n}^{(1)}$. We then motivate and propose conjectures for the relationship between the specialized Macdonald polynomial and Demazure characters in type $C_{n}^{(1)}$.

Free pizzas as always:)