论文标题
比较类型中的fock空间$ a^{（1）} $和$ a^{（2）} $
Comparing Fock spaces in types $A^{(1)}$ and $A^{(2)}$
论文作者
论文摘要
We compare the canonical bases of level-$1$ quantised Fock spaces in affine types $A^{(1)}$ and $A^{(2)}$, showing how to derive the canonical basis in type $A^{(2)}_{2n}$ from the the canonical basis in type $A^{(1)}_n$ in certain weight spaces.特别是，我们在极端重量空间中为规范基础得出一个明确的公式，这对应于对称组的双层盖的岩石块。在即将发表的Kleshchev和Morotti的论文中，我们将使用此公式来找到带有Abelian缺陷的双层盖岩石块的分解编号。
We compare the canonical bases of level-$1$ quantised Fock spaces in affine types $A^{(1)}$ and $A^{(2)}$, showing how to derive the canonical basis in type $A^{(2)}_{2n}$ from the the canonical basis in type $A^{(1)}_n$ in certain weight spaces. In particular, we derive an explicit formula for the canonical basis in extremal weight spaces, which correspond to RoCK blocks of double covers of symmetric groups. In a forthcoming paper with Kleshchev and Morotti we will use this formula to find the decomposition numbers for RoCK blocks of double covers with abelian defect.
