Cylindric skew Schur functions

• Autores: Peter McNamara
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 205, Nº 1, 2006, págs. 275-312
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov¿Witten invariants. After explaining these motivations, we study cylindric skew Schur functions from the point of view of Schur-positivity. Using a result of I. Gessel and C. Krattenthaler, we generalise a formula of A. Bertram, I. Ciocan-Fontanine and W. Fulton, thus giving an expansion of an arbitrary cylindric skew Schur function in terms of skew Schur functions. While we show that no non-trivial cylindric skew Schur functions are Schur-positive, we conjecture that this can be reconciled using the new concept of cylindric Schur-positivity.