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The center of the twisted Heisenberg category, factorial Schur Q-functions, and transition functions on the Schur graph

  • Henry Kvinge
  • Can Ozan Oğuz
  • Michael ReeksEmail author
Article
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Abstract

We establish an isomorphism between the center of the twisted Heisenberg category and the subalgebra \(\Gamma \) of the symmetric functions generated by odd power sums. We give a graphical description of the factorial Schur Q-functions and inhomogeneous power sums as closed diagrams in the twisted Heisenberg category and show that the bubble generators of the center correspond to two sets of generators of \(\Gamma \) which encode data related to up/down transition functions on the Schur graph. Finally, we describe an action of the trace of the twisted Heisenberg category, the W-algebra \(W^-\subset W_{1+\infty }\), on \(\Gamma \).

Keywords

Hecke algebras Spin representation theory Schur Q-functions Schur graph 

Notes

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Authors and Affiliations

  1. 1.Pacific Northwest National LaboratorySeattleUSA
  2. 2.Galatasaray UniversityIstanbulTurkey
  3. 3.Bucknell UniversityLewisburgUSA

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