Temperley-Lieb pfaffinants and Schur Q-positivity conjectures

• Autores: Thomas Lam, Pavlo Pylyavskyy
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 5, 2008, págs. 1654-1684
• Idioma: inglés
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• Resumen

  • 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