2026/2027

Симметрические функции и представления группы S_n

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 3, 4 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Куюмжиян Каринэ Георгиевна

Язык: английский

Кредиты: 6

Контактные часы: 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+