Introduction to Quantum Groups

A-algebra a-orbit A-submodule A₁ algebra homomorphism Assume automorphism b₁ b₂ based module Bi;n bijection bilinear braid group canonical basis Cartan datum CHAPTER coefficient coinvariants commutative Corollary deduce defined definition denote dim G/Q dim V₁ direct sum equal equivalent finite dimensional finite type full subcategory functor given graph hence identity induction hypothesis inner product integrable U-module involution isomorphism K(Qv lemma is proved linear map mod v¯¹L(f morphism non-zero Note obtain pairing perverse sheaves proof proposition is proved Q(v)-algebra Q(v)-vector space QT,w quantum quotient reduced expression resp root datum RỦ satisfies sequence Serre relations signed basis simple object structure subset subspace summand surjective symmetric T₁ tensor product Theorem unique element v-¹L v¯¹A vector space Verma module well-defined Y-regular zero