Temperley-Lieb pfaffinants and Schur Q-positivity conjectures

Thomas Lam, Pavlo Pylyavskyy

Research output: Contribution to journalArticlepeer-review


We study pfaffian analogues of immanants, which we call pfaffinants. Our main object is the TL-pfaffinants which are analogues of Rhoades and Skandera's TL-immanants. We show that TL-pfaffinants are positive when applied to planar networks and explain how to decompose products of complementary pfaffians in terms of TL-pfaffinants. We conjecture in addition that TL-pfaffinants have positivity properties related to Schur Q-functions.

Original languageEnglish (US)
Pages (from-to)1654-1684
Number of pages31
JournalAdvances in Mathematics
Issue number5
StatePublished - Aug 1 2008

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: tfylam@math.harvard.edu (T. Lam), pasha@math.mit.edu (P. Pylyavskyy). 1 Partially supported by NSF DMS-0600677.


  • Network positivity
  • Pfaffian
  • Schur Q-function
  • Temperley-Lieb immanants


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