Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex model

Korff, C. (2021) Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex model. Communications in Mathematical Physics, 381(2), pp. 591-640. (doi: 10.1007/s00220-020-03906-x)

[img] Text
221683.pdf - Published Version
Available under License Creative Commons Attribution.



We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as structure constants the 3-point genus zero Gromov–Witten invariants of Grassmannians and are spanned by what we call cylindric Hecke characters, a particular set of virtual characters for whose computation we give several explicit combinatorial formulae. One of these expressions is a generalisation of Ram’s formula for irreducible Hecke characters and uses cylindric broken rim hook tableaux. We show that the latter are in bijection with so-called ‘ice configurations’ on a cylindrical square lattice, which define the asymmetric six-vertex model in statistical mechanics. A key ingredient of our construction is an extension of the boson-fermion correspondence to Hecke algebras and employing the latter we find new expressions for Jing’s vertex operators of Hall–Littlewood functions in terms of the six-vertex transfer matrices on the infinite planar lattice.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Korff, Professor Christian
Authors: Korff, C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
ISSN (Online):1432-0916
Published Online:24 December 2020
Copyright Holders:Copyright © 2020 The Author
First Published:First published in Communications in Mathematical Physics 381(2): 591-640
Publisher Policy:Reproduced under a Creative Commons License
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record