English

Temperley-Lieb pfaffinants and Schur $Q$-positivity conjectures

Combinatorics 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0612842,
  title  = {Temperley-Lieb pfaffinants and Schur $Q$-positivity conjectures},
  author = {Thomas Lam and Pavlo Pylyavskyy},
  journal= {arXiv preprint arXiv:math/0612842},
  year   = {2007}
}

Comments

30 pages, 13 figures