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Some webs and q-Howe dualities in types BCD

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HTLW04 - Quantum topology and categorified representation theory

Co-author: Antonio Sartori (University of Freiburg)

In seminal work, Cautis-Kamnitzer-Morrison gave a diagrammatic presentation, via a so-called web calculus, of the category of quantum gln modules tensor generated by the exterior powers. Their novel observation was that a classical tool from representation and invariant theory, known as skew Howe duality, can be quantized and used to construct the corresponding diagrammatic presentation.

The work of Cautis-Kamnitzer-Morrison was then extended to various other instance (and even categorified), but all of these have in common that they stay in type A.

In this talk I will describe the first steps towards generalizing Cautis-Kamnitzer-Morrison's results to other types, where several new features (or flaws?) appear.

This talk is part of the Isaac Newton Institute Seminar Series series.

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