A Mackey decomposition theorem and cohomology for quantum groups at roots of 1
The author proves a special Mackey decomposition theorem over a field for quantum groups. Using this theorem, he studies the structure of \(R^ 1 \text{ Ind}^ U_{U^{\leq 0} \leq 0}\lambda\) and the nonvanishing property of certain \(R^ i \text{ Ind}^ U_{U^{\leq 0} \leq 0} \lambda\). Moreover, he studies the good filtration of \(U\)-modules and gets a theorem for quantum groups at roots of 1, which describes all composition factors of \(\text{Ind}^ U_{U^{\leq 0} \leq 0} \lambda\) and was first proved for algebraic groups by the reviewer, where \(U\) is the quantum enveloping algebra and \(U^{\leq 0}\) is its subalgebra.
scientific article; zbMATH DE number 614253