Extensions of simple modules for quantum groups at complex roots of $1$
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Key Points
Extension groups for simple modules are governed by a finite subset of small highest weights, indicating a deeper structure.
For quantum groups at roots of unity, dimensions of extension groups match top degree coefficients of Kazhdan-Lusztig polynomials for affine Weyl groups.
The problem is shown to relate extensions between simple modules in quantum groups and their small quantum groups, highlighting their relationship.
Results connect similar findings for almost simple algebraic groups to their Frobenius subgroup schemes, enriching our understanding of representation theory.
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Implication
This analysis reveals extension groups of simple modules in quantum groups, indicating connections to Kazhdan-Lusztig polynomials.
Cite This Study
Henning Haahr Andersen (2025) studied this question.