Adding \pm 1 to the argument of an Hall-Littlewood polynomial

Alain Lascoux (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Shifting by \pm 1 powers sums: p_i \to p_i \pm 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane partitions, as well as some generating functions. We recover in particular an identity of Warnaar related to Rogers-Ramanujan identities.

Mots clés: Hall-Littlewood polynomials

Domaines: Combinatoire [math.CO]

Alain Lascoux. Adding \pm 1 to the argument of an Hall-Littlewood polynomial. 2007. ⟨hal-00171973⟩