Refined Cauchy and Littlewood identities, plane partitions, and partition functions in the six-vertex model

par Michael Wheeler (LPTHE Paris)

jeudi 6 févr. 2014, 11:00 → 12:00 Europe/Paris

Auditorium (Annecy-le-Vieux)

In the theory of symmetric functions, it is well known that Cauchy or Littlewood identities can be interpreted as generating series for plane partitions with specific weightings. For example, in the case of Schur functions, an appropriate specialization of the Cauchy identity leads to the MacMahon generating series for volume-weighted plane partitions. In this talk we will show that certain Cauchy and Littlewood identities admit "refined" versions, which evaluate to partition functions of the six-vertex model, on relevant domains. This allows us to relate certain generating series of plane partitions to appropriate symmetry classes of alternating sign matrices. We will discuss three such examples in the talk.

Slides LAPTh_talk_Wheeler.pdf