Temperley-Lieb pfaffinants and Schur Q-positivity conjectures |
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| Authors: | Thomas Lam Pavlo Pylyavskyy |
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| Institution: | a Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
b University of Michigan, Department of Mathematics, 530 Church Street, Ann Arbor, MI, USA |
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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. |
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| Keywords: | Schur Q-function Pfaffian Network positivity Temperley-Lieb immanants |
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