Maulik-Okounkov Lie Algebras and BPS Lie Algebras

Explore the connections between Maulik-Okounkov (MO) Lie algebras and BPS Lie algebras in this advanced mathematics lecture. Delve into the R-matrix formalism developed by Maulik and Okounkov for quantum cohomology of Nakajima quiver varieties, and examine the origins of BPS Lie algebras in cohomological Donaldson-Thomas theory. Learn how to identify the MO Lie algebra of a quiver Q with the BPS Lie algebra of the tripled quiver Q̃ using its canonical cubic potential. Discover the role of non-abelian stable envelopes in bridging these two mathematical worlds and relating their representations. Gain insights into Okounkov's conjecture, which equates the graded dimensions of the MO Lie algebra with Kac polynomial coefficients. This in-depth talk presents joint work with Ben Davison, offering a comprehensive exploration of cutting-edge research in algebraic geometry and representation theory.