Quasi-hereditary slim cyclotomic q-Schur algebras
Quasi-hereditary slim cyclotomic q-Schur algebras
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DOI：
10.1016/j.jpaa.2023.107354
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发表时间：
2023-02
影响因子：
0.8
通讯作者：
B. Deng;Guiyu Yang
中科院分区：
文献类型：
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作者：
B. Deng;Guiyu Yang
细长切环q-Schur代数是Dipper、James和Mathas意义上切环q-Schur代数的若干中心化子代数，包括A型和C型q-Schur代数为例。本文给出了细长切环q-Schur代数m （n, r）是拟遗传的一个充分条件。更确切地说，如果切环Hecke代数有半单底，则证明了m （n, r）是准遗传的。此外，我们证明m （1, r）是拟遗传的当且仅当切环Hecke代数有半单底。在m= n= r= 2, q=±1的情况下，证明了这个条件也是必要的。
Slim cyclotomic q-Schur algebras are certain centralizer subalgebras of cyclotomic q-Schur algebras in the sense of Dipper, James and Mathas, including q-Schur algebras of type A and C as examples. In the present paper we provide a sufficient condition for a slim cyclotomic q-Schur algebra S m (n, r) to be quasi-hereditary. More precisely, it is shown that S m (n, r) is quasi-hereditary if the cyclotomic Hecke algebra has a semisimple bottom. Moreover, we prove that S m (1, r) is quasi-hereditary if and only if the cyclotomic Hecke algebra has a semisimple bottom. In the case where m= n= r= 2 and q=±1, we prove that this condition is also necessary.