Temperley-Lieb pfaffinants and Schur Q-positivity conjectures

Thomas Lam; Pavlo Pylyavskyy

doi:10.1016/j.aim.2008.03.027

Temperley-Lieb pfaffinants and Schur Q-positivity conjectures

Thomas Lam, Pavlo Pylyavskyy

Mathematics

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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.

Original language	English (US)
Pages (from-to)	1654-1684
Number of pages	31
Journal	Advances in Mathematics
Volume	218
Issue number	5
DOIs	https://doi.org/10.1016/j.aim.2008.03.027
State	Published - 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.

Keywords

Network positivity
Pfaffian
Schur Q-function
Temperley-Lieb immanants

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AU - Pylyavskyy, Pavlo

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KW - Pfaffian

KW - Schur Q-function

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Temperley-Lieb pfaffinants and Schur Q-positivity conjectures

Abstract

Bibliographical note

Keywords

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