Affine Grassmannian slices are varieties which appear naturally in
geometric representation theory. Their quantisations are given by truncated
shifted Yangians. I will describe a recent result which gives an equivalence of
categories between modules for truncated shifted Yangians and modules for
Khovanov-Lauda-Rouquier-Webster algebras. We use this theorem to a) resolve a
conjecture describing the highest weights of truncated shifted Yangians, and b)
prove the so-called "symplectic duality" between affine Grassmannian slices and
Nakajima quiver varieties in the simply-laced cases. The latter result provides
a link between two very different geometric models for representations of
semisimple Lie algebras. This is joint work with Kamnitzer, Tingley, Webster,
and Weekes.
About Pure mathematics seminars
We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.
Seminars are usually held on Tuesdays from 2 to 3pm.
Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.
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Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.
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To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.