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arXiv · 1802.08977

Cylindric Reverse Plane Partitions and 2D TQFT

Christian Korff·David Palazzo
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Abstract

The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\lambda$ 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 cylindric complete symmetric functions to a 2D topological quantum field theory (TQFT) that is a generalisation of the celebrated $\mathfrak{\widehat{sl}}_n$-Verlinde algebra or Wess-Zumino-Witten fusion ring, which plays a prominent role in the context of vertex operator algebras and algebraic geometry.

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BibTeXRIS

Christian Korff, David Palazzo. 2018-02-25. Cylindric Reverse Plane Partitions and 2D TQFT. https://arxiv.org/abs/1802.08977

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