Cylindric reverse plane partitions and 2D TQFT

Korff, C. and Palazzo, D. (2018) Cylindric reverse plane partitions and 2D TQFT. Séminaire Lotharingien de Combinatoire, 80B, 30.

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The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions one arrives at weighted sums over reverse plane partitions (RPP) involving binomial coefficients. Employing the action of the extended affine symmetric group at fixed level n we generalise these weighted sums to cylindric RPP and define cylindric complete symmetric functions. The latter are shown to be h-positive, that is, their expansions coefficients in the basis of complete symmetric functions are non-negative integers. We state an explicit formula in terms of tensor multiplicities for irreducible representations of the generalised symmetric group. Moreover, we relate the complete symmetric functions to a 2D topological quantum field theory (TQFT) that is a generalisation of the celebrated sl_n-Verlinde algebra or Wess–Zumino–Witten fusion ring, which plays a prominent role in the context of vertex operator algebras and algebraic geometry.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Palazzo, Mr David and Korff, Professor Christian
Authors: Korff, C., and Palazzo, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Séminaire Lotharingien de Combinatoire
Publisher:Université Louis Pasteur
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