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

Kvinge H., OĞUZ C. O., Reeks M.

30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018, New Hampshire, Amerika Birleşik Devletleri, 16 - 20 Temmuz 2018 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: New Hampshire
  • Basıldığı Ülke: Amerika Birleşik Devletleri
  • Anahtar Kelimeler: Heisenberg categorification, Spin representation theory of symmetric groups, Symmetric functions
  • Galatasaray Üniversitesi Adresli: Evet

Özet

We establish an isomorphism between the center EndHtw(1) of the twisted Heisenberg category of Cautis and Sussan and G, 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 G 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.