论文标题
朝吉亚人有限维度的杆子
Poles of finite-dimensional representations of Yangians
论文作者
论文摘要
令$ \ mathfrak {g} $为有限的简单谎言lie代数，超过$ \ mathbb {c} $，让$ y _ _ {\ hbar}（\ mathfrak {g}）$是$ \ sathfrak {g} $的yangian of yangian of yangian。在本文中，我们研究了定义$ y _ {\ hbar}（\ mathfrak {g}）$的作用的有理电流的杆子集。使用Frenkel和Hernandez的Baxter多项式性的弱，理性的版本，我们根据编码$ V $的组成因子的Drinfeld多项式来获得这些集合的统一描述，以及$ Q $ -CARTAN MATRIX的$ \ Mathfrak {G} g} $。然后，我们应用此描述以获得一组充分条件的混凝土集，以使任何两个不可约表示的张量产物的张量和简单性，并对日格双重双重的有限维度不可减至表示分类。
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 study the sets of poles of the rational currents defining the action of $Y_{\hbar}(\mathfrak{g})$ on an arbitrary finite-dimensional vector space $V$. Using a weak, rational version of Frenkel and Hernandez' Baxter polynomiality, we obtain a uniform description of these sets in terms of the Drinfeld polynomials encoding the composition factors of $V$ and the inverse of the $q$-Cartan matrix of $\mathfrak{g}$. We then apply this description to obtain a concrete set of sufficient conditions for the cyclicity and simplicity of the tensor product of any two irreducible representations, and to classify the finite-dimensional irreducible representations of the Yangian double.
