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Disquisitions on Monoidal Categories and Operads
Disquisitions on Monoidal Categories and Operads
A categorification of Grothendieck differential operators on the affine line
A categorification of Grothendieck differential operators on the affine line
Organizers
Speaker
Cailan Li
Time
Monday, May 11, 2026 4:00 PM - 5:00 PM
Venue
A3-1-301
Online
Zoom 559 700 6085
(BIMSA)
Abstract
Given a Hopf pairing between two bialgebras $K$ and $G$, one can define the Hesienberg double $h(G)$, which recovers the classical Heisenberg algebra in the case $K=G=Sym$, the ring of symmetric functions in infinitely many variables. A classical result of Geissinger identifies $Sym$ with the grothendieck ring $K_0$ on the tower of group algebras of the symmetric group $\oplus_n C[S_n]$. Replacing this tower of symmetric group algebras by a tower $T$ of (finite-dimensional) algebras satisfying certain axioms, Savage and Yacobi constructed a categorification of $h(K_0(T))$ acting on its Fock space representation. In this talk we will extend this framework to towers of infinite-dimensional algebras and as an application, categorify the action of Grothendieck differential operators acting on $A^1_{Z[v,v^{-1}]}$.
This talk is based on joint work with Chun-Ju Lai.
This talk is based on joint work with Chun-Ju Lai.