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.
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* Corresponding author. E-mail addresses: firstname.lastname@example.org (T. Lam), email@example.com (P. Pylyavskyy). 1 Partially supported by NSF DMS-0600677.
- Network positivity
- Schur Q-function
- Temperley-Lieb immanants