Nikolaus Conference 2018

Speaker: Rekha Biswal (Bonn)

Title: Affine Structure and Tableaux Models for \(E_7\) Crystals


A Kirillov-Reshetikhin (KR) module is a certain finite dimensional \(U_q'(\mathfrak{g})\) module that is determined by its Drinfeld polynomials. KR modules are an important class of modules for quantum groups with many applications to Mathematical physics. KR modules are conjectured to have many nice properties, one of which is the existence of a crystal basis. In this talk, we will give a unique affine crystal structure for the type \(E_7^1\) KR crystals corresponding to the multiples of fundamental weights \(s\Lambda_7\) for all \(s \geq 1\). This is based on ongoing joint work with Travis Scrimshaw.

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