Logarithmic and complex constant term identities

Tom Chappell , Alain Lascoux (1) , S. Ole Warnaar , Wadim Zudilin

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamovic and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove complex and logarithmic constant term identities for the root system G_2.

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]; Algèbres quantiques [math.QA]

Tom Chappell, Alain Lascoux, S. Ole Warnaar, Wadim Zudilin. Logarithmic and complex constant term identities. Computational and Analytical Mathematics, Springer, pp.219-250, 2013, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-1-4614-7621-4_11⟩. ⟨hal-00826211⟩