Finite-dimensional representations of Yangians in complex rank

2018/05/29 by Kalinov, Daniil
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.11639

Abstract

We classify the "finite-dimensional" irreducible representations of the Yangians Y(\mathfrakgl_t) and Y(\mathfraksl_t). These are associative ind-algebras in the Deligne category Rep(GL_t), which generalize the regular Yangians Y(\mathfrakgl_n) and Y(\mathfraksl_n) to complex rank. They were first defined by Etingof in his paper "Representation theory in complex rank". Here we solve Problem 7.2 from this paper. We work with the Deligne category Rep(GL_t) using the ultraproduct approach introduced by Deligne and discussed by Nate Harman in arXiv:1601.03426.

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