2026/2027

Symmetric Functions and Representations of S_n

ID 1251586

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Karine Kuyumzhiyan

Language: English

ECTS credits: 6

Contact hours: 72

Course Syllabus

Abstract

The theory of symmetric functions is one of the central branches of algebraic combinatorics. Being a rich and beautiful theory by itself, it also has numerous connections with the representation theory and algebraic geometry (especially representation theory of finite or classical groups and geometry of homogeneous spaces). In this course we will mostly focus on the combinatorial aspects of the theory of symmetric functions and study the properties of Schur polynomials. In representation theory they appear as characters of representations of $GL(n)$; they are also closely related with the geometry of Grassmannians. We will prove that the character table of $S_n$ coincides with the transition matrix between $p_\lambda$ and $s_\lambda$. We will also discuss Schubert polynomials. 2+