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SUMMARY:Maulik-Okounkov Lie algebras  and BPS Lie algebras - Tommaso Maria
  Botta (ETH Zurich)
DTSTART:20240620T135000Z
DTEND:20240620T143000Z
UID:TALK217714@talks.cam.ac.uk
DESCRIPTION:The Maulik-Okounkov Lie algebra associated to a quiver Q contr
 ols the R-matrix formalism developed by Maulik and Okounkov in the context
  of quantum cohomology of Nakajima quiver varieties. On the other hand\, t
 he BPS Lie algebra originates from cohomological DT theory\, particularly 
 from the theory of cohomological Hall algebras associated with 3 Calabi-Ya
 u categories. In this talk\, I will explain how to identify the MO Lie alg
 ebra of Q with the BPS Lie algebra of the tripled quiver Q̃ with its cano
 nical cubic potential. The bridge to compare these similarly diverse words
  is the theory of non-abelian stable envelopes\, which can be exploited to
  relate representations of the MO Lie algebra to representations of the BP
 S Lie algebra. In conclusion\, I will explain how to use these results to 
 deduce Okounkov's conjecture\, equating the graded dimensions of the MO Li
 e algebra with the coefficients of Kac polynomials. This is joint work wit
 h Ben Davison.
LOCATION:Seminar Room 1\, Newton Institute
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