Cohomology in Singular Blocks for a Quantum Group at a Root of Unity
Cohomology in Singular Blocks for a Quantum Group at a Root of Unity
Let $U_\zeta$ be a Lusztig quantum enveloping algebra associated to a complex semisimple Lie algebra $\mathfrak g$ and a root of unity $\zeta$. When $L,L'$ are irreducible $U_\zeta$-modules having regular highest weights, the dimension of $\operatorname{Ext}^n_{U_\zeta}(L,L')$ can be calculated in terms of the coefficients of appropriate Kazhdan-Lusztig polynomials associated to …