A(1)和A(2)类型的Fock空间比较

Q3 Mathematics

Algebraic Combinatorics Pub Date : 2023-11-07 DOI:10.5802/alco.300

Matthew Fayers

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引用次数: 0

摘要

我们比较了仿射类型A(1)和A(2)的一级量子化Fock空间的正则基，展示了如何从某些权重空间中A (n(1)型的正则基推导出A (2n(2)型的正则基。特别地，我们导出了对应于对称群的双盖的RoCK块的极值权空间中正则基的显式公式。在与Kleshchev和Morotti合著的一篇即将发表的论文中，我们将使用该公式求出具有阿贝尔缺陷的双盖岩块的分解数。

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Comparing Fock spaces in types A (1) and A (2)

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 2n (2) from the the canonical basis in type A n (1) 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.

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来源期刊

Algebraic Combinatorics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

51 weeks