Séminaire Lotharingien de Combinatoire, 80B.76 (2018), 12 pp.
Henry Kvinge, Can Ozan Oğuz, and Michael Reeks
The Center of the Twisted Heisenberg Category, Factorial P-Schur Functions, and Transition Functions on the Schur Graph
Abstract.
We establish an isomorphism between the center EndHtw(1) of the twisted
Heisenberg category of Cautis and Sussan and Γ, the subalgebra
of the symmetric functions generated by odd power sums. We give a
graphical description of Ivanov's factorial Schur P-functions as
closed diagrams in Htw and show that the curl
generators of EndHtw(1) correspond to two sets of generators of
Γ discovered by Petrov which encode data related to up/down
transition functions on the Schur graph. Our results are a twisted
analogue of those of Kvinge, Licata, and Mitchell, which related the
center of Khovanov's Heisenberg category to the algebra of shifted
symmetric functions.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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