Dual Perfect Bases and dual perfect graphs
Dual Perfect Bases and dual perfect graphs
复制标题
双完美基础和双完美图表
DOI：
10.17323/1609-4514-2015-15-2-319-335
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
U. Suh
中科院分区：
文献类型：
--
作者：
Byeong Hoon Kahng;Seok;M. Kashiwara;U. Suh
我们引入了对偶完美基和对偶完美图的概念。证明了量子广义Kac-Moody代数U_{q}（\mathcal{g}）$上的每个可积最高权模V_q（\lambda）$都有一个对偶完美基，并且它的对偶完美图同构于晶体B（\lambda）$.我们还证明了负半$U_{q}^{-}（\mathcal{g}）$有一个对偶完美基，其对偶完美图同构于晶体$B（\infty）$。更一般地，我们证明了所有的对偶完美图的一个给定的对偶完美空间是同构的抽象晶体。最后，我们证明了Khovanov-Lauda-Rouquier代数上的分次生成分次投射不可分解模的同构类与其分圆子构成其Grothendieck群的对偶完美基.
We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q(\lambda)$ over a quantum generalized Kac-Moody algebra $U_{q}(\mathcal{g})$ has a dual perfect basis and its dual perfect graph is isomorphic to the crystal $B(\lambda)$. We also show that the negative half $U_{q}^{-}(\mathcal{g})$ has a dual perfect basis whose dual perfect graph is isomorphic to the crystal $B(\infty)$. More generally, we prove that all the dual perfect graphs of a given dual perfect space are isomorphic as abstract crystals. Finally, we show that the isomorphism classes of finitely generated graded projective indecomposable modules over a Khovanov-Lauda-Rouquier algebra and its cyclotomic quotients form dual perfect bases for their Grothendieck groups.