# Prologue {-} ## References - Carter's "Finite Groups of Lie Type"[@carter_1985] - Humphreys' "Linear Algebraic Groups"[@humphreys_2004] - Course Videos: ## Notation \todo[inline]{Todo} \newpage ## Outline Guide for Math 8190 Videos: [9-14-20] A survey on the representation theory of finite-dimensional algebras [9-25-20] Frobenius kernels, simple G_r-modules, Steinberg's Tensor Product Theorem, Connections with Lusztig's Conjecture [9-28-20] Kempf's Vanishing Theorem, Good and Weyl filtrations, Cohomology [10-2-20] Good and Weyl Filtrations [10-5-20] Highest Weight Categories [10-7-20] Examples: Schur algebras, tilting modules, Weyl modules, Bott-Borel-Weil Theorem [10-9-20] Bott-Borel-Weil Theory [10-12-20] Bott-Borel-Weil Theorem with applications [10-14-20] Basic Properties of Characters, Weyl's Character Formula [10-16-20] Weyl's Character Formula [10-19-20] Linkage, Strong Linkage, Examples [10-21-20] Strong Linkage Principle, Translation Functors (intro) [10-23-20] Translation Functors [10-26-20] Translation Functors and Characters [10-28-20] Properties of Translation Functors [11-2-20] Translation, Wall Crossing, Lusztig's Conjecture [11-4-20] Representations of G_rT and G_rB [11-6-20] Representations of G_rT and G_rB, Good (p,r)-filtrations, Donkin's (p,r)-Filtration Conjecture [11-9-20] Strong Linkage for G_rT-modules, Extensions for G_rT-modules, Steinberg Modules [11-11-20] Filtrations and Reciprocity for G_rT and G_r Modules [11-13-20] G_rT-modules and reciprocity, Injective G_rT-modules, Humphreys-Verma Conjecture, Donkin's Tilting Module Conjecture [11-16-20] G-structures for injective G_r-modules, Donkin's Tilting Module Conjecture [11-18-20] Injective G_T-modules and Injective G-modules [11-20-20] Cohomology of Frobenius kernels, finite generation of cohomology [11-23-20] Cohomology of Frobenius kernels, restricted nullcone, Jantzen's Conjecture on support varieties, conjectures for low primes