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- W3086906863 abstract "Let $mathfrak{g}$ be a finite-dimensional simple Lie algebra over $mathbb{C}$, and let $Y_{hbar}(mathfrak{g})$ be the Yangian of $mathfrak{g}$. In this paper, we initiate the study of the set of poles of the rational currents defining the action of $Y_{hbar}(mathfrak{g})$ on an arbitrary finite-dimensional vector space $V$. We prove that this set is completely determined by the eigenvalues of the commuting Cartan currents of $Y_{hbar}(mathfrak{g})$, and therefore encodes the singularities of the components of the $q$-character of $V$. In type $mathsf{A}$, we explicitly determine the set of poles of every irreducible $V$ in terms of the roots of the underlying Drinfeld polynomials. In particular, our results yield a complete classification of the finite-dimensional irreducible representations of the Yangian double in type $mathsf{A}$." @default.
- W3086906863 created "2020-09-21" @default.
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- W3086906863 creator A5074913079 @default.
- W3086906863 date "2020-09-14" @default.
- W3086906863 modified "2023-09-27" @default.
- W3086906863 title "Poles of finite-dimensional representations of Yangians in type A" @default.
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