Logarithmic and Complex Constant Term Identities

  • Tom Chappell
  • Alain Lascoux
  • S. Ole Warnaar
  • Wadim ZudilinEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 50)


In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2, p), Adamović 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 Adamović 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 such identities for the root system G2.

Key words

Constant term identities Jon’s birthday Perfect matchings Pfaffians Root systems 

Mathematics Subject Classifications (2010)

Primary 05E05 Secondary 05A05 05A10 05A19 33C20 



The authors have greatly benefited from Tony Guttmann’s and Vivien Challis’ expertise in numerical computations. The authors also thank Antun Milas and the anonymous referee for very helpful remarks, leading to the inclusion of Sect. 11.6.3. OW and WZ are supported by the Australian Research Council.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tom Chappell
    • 1
  • Alain Lascoux
    • 2
  • S. Ole Warnaar
    • 1
  • Wadim Zudilin
    • 3
    Email author
  1. 1.School of Mathematics and PhysicsThe University of QueenslandBrisbaneAustralia
  2. 2.CNRS, Institut Gaspard Monge, Université Paris-EstMarne-la-ValléeFrance
  3. 3.School of Mathematical and Physical SciencesThe University of NewcastleCallaghanAustralia

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