Scheda programma d'esame
GRUPPI E RAPPRESENTAZIONI
GIOVANNI GAIFFI
Anno accademico2017/18
CdSMATEMATICA
Codice057AA
CFU6
PeriodoSecondo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
GRUPPI E RAPPRESENTAZIONIMAT/02LEZIONI48
GIOVANNI GAIFFI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge

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

Assessment criteria of knowledge

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.

Methods:

  • Final oral exam

 

Skills

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).

Assessment criteria of skills

Many excercises will be solved together with the students during the lessons.

Teaching methods

Delivery: face to face

Attendance: Advised

Learning activities:

  • attending lectures
  • individual study

 

Teaching methods:

  • Lectures

 

Syllabus

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

Work placement

Yes

Ultimo aggiornamento 29/09/2017 08:11