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

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

2006-12-28

arxiv.org/abs/math/0612842v1

Mathematics

Combinatorics

30 pages, 13 figures

Scientific paper

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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