Kirillov–Reshetikhin Conjecture: The General Case
Kirillov–Reshetikhin Conjecture: The General Case
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基里洛夫-列舍季欣猜想：一般情况
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发表时间：
2007
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通讯作者：
D. Hernandez
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文献类型：
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作者：
D. Hernandez
在一般情况下证明了Kirillov-Reshetikhin（KR）猜想：对于所有的扭量子仿射代数，我们证明了KR模的特征标解扭Q-系，并得到了它们张量积的特征标的显式公式（Najakima处理了无扭的简单花边情形，作者处理了无扭情形）.这个证明是统一的，并且为扭曲量子仿射代数的表示理论提供了几个新的发展，包括扭曲的Frenkel-Reshetikhin q-特征标（Frenkel-Reshetikhin和Frenkel-Mukhin预期的）。我们还证明了扭曲T系统。作为应用，我们得到了所有类型的基本表示的扭曲q-特征标的显式公式，包括Reshetikhin给出的D_4^{（3）}，E_6^{（2）}型的公式。本文证明了Kuniba-Suzuki给出的A_n^{（2）}和D_4^{（3）}型KR模的计算公式。最终我们的结果将分支规则[HKOTT]推广到有限型量子子代数上。
We prove the Kirillov-Reshetikhin (KR) conjecture in the general case : for all twisted quantum affine algebras we prove that the characters of KR modules solve the twisted Q-system and we get explicit formulas for the character of their tensor products (the untwisted simply-laced case was treated by Najakima, and the untwisted case by the author). The proof is uniform and provides several new developments for the representation theory of twisted quantum affine algebras, including twisted Frenkel-Reshetikhin q-characters (expected by Frenkel-Reshetikhin and Frenkel-Mukhin). We also prove the twisted T-system. As an application we get explicit formulas for the twisted q-characters of fundamental representations for all types, including the formulas for types D_4^{(3)}, E_6^{(2)} conjectured by Reshetikhin. We prove the formulas for KR modules in types A_n^{(2)} and D_4^{(3)} conjectured by Kuniba-Suzuki. Eventually our results imply the conjectural branching rules [HKOTT] to the quantum subalgebra of finite type.