Introduction to Quantum Groups

a-orbit A-submodule a₁ algebra homomorphism Assume automorphism b₁ b₂ based module bijection braid group canonical basis Cartan datum CHAPTER coefficient coinvariants commutative Corollary deduce defined definition denote direct sum direct sum decomposition equal equivalent finite dimensional finite type following result functor given graph hence highest weight identity induction hypothesis inner product involution isomorphism K(Qv left ideal lemma is proved linear map mod v-¹L mod v¯¹L(f morphism non-zero Note obtain pairing perverse sheaves previous lemma proof proposition is proved Q(v)-algebra quantum quotient R-algebra reduced expression resp root datum RỦ satisfies semisimple sequence Serre relations signed basis simple object structure subset subspace suffices summand surjective symmetric T₁ tensor product Theorem unique element v¯¹A vector space Verma module well-defined Y-regular zero