Affinization of category O for quantum groups
Affinization of category O for quantum groups
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DOI：
10.1090/s0002-9947-2014-06039-x
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发表时间：
2012-04
影响因子：
1.3
通讯作者：
E. Mukhin;Charles Young
中科院分区：
文献类型：
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作者：
E. Mukhin;Charles Young
令 g 为一个简单的李代数。我们考虑仿射量子群 Uq(g-hat) 上这些模块的类别 O-hat，其 Uq(g) 权重具有有限重数，并且位于由负根生成的锥体的有限并集中。我们证明了有限维表示范畴的许多属性自然地扩展到 O 帽范畴。特别是，我们发展了 q 字符理论并定义了抛物线 Verma 模块的最小亲和力。在 ABCFG 类型中，我们对这些最小亲和关系进行分类，并推测其特征的 Weyl 分母类型公式。
Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category O-hat. In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.