|GRUPPI E RAPPRESENTAZIONI||MAT/02||LEZIONI||48|
knowledge of the basics of representation theory of finite groups knowledge of the representation theory of the symmetric group: young diagrams and tableaux, characters, etc knowledge of the representation theory of the algebraic representation of the general linear group
During the written and oral exam the student must be able to demonstrate his/her knowledge of the course material and be able to discuss the reading matter thoughtfully and with propriety of expression, and to solve simple exercises.
- Final oral exam
The student will be able to work with representations of finite groups and to apply his knowledge also in several geometric settings (action on homologous, cohomology, study of finite groups generated by reflections).
Many excercises will be solved together with the students during the lessons.
Delivery: face to face
- attending lectures
- individual study
representation theory of finite groups: definition, subrepresentation, irreducible representation, quotients complete reducibility, Schur's lemma characters, and orthonormality of the characters of irreducible representation induction Groups generated by reflections Representation of associative algebras, semisimple algebras representation of the symmetric group: construction of representations and characters Schurs' duality Algebraic Representations of the general linear group