Macdonald Polynomials and Gram-Schmidt in Derived Categories

Anton Khoroshkin (Haifa University)

Wednesday 13th September, 2023 16:00-17:00 Maths 110


In this talk, I will begin by recalling the Macdonald pairings and Macdonald polynomials, which are symmetric functions that are pairwise orthogonal under this specific pairing.
Next, I will propose an interpretation of this pairing, based on the representations of the Lie algebra of currents.
Subsequently, I will elucidate the Gram-Schmidt algorithm within the corresponding derived category.
As a culmination of these discussions, I will unveil a collection of modules whose characters coincide with Macdonald polynomials, subject to specific substitutions.

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