Representation Theory
Short Course on
Interpolation Polynomials and Representation Theory
University of Isfahan
December 31, 2019
Moderator: Malihe Yousofzadeh (
2 Lectures
Title: Interpolation Polynomials and Representation Theory
Instructor: Hadi Salmasian (University of Ottawa, Canada)
Date: Tuesday, December 31, 2019
Time: 14:30 - 16:00 & 16:30 - 18:00
Venue: Department of Mathematical Sciences, Seminar Room 3

This self-contained mini-course will cover recent progress on connections between interpolation symmetric polynomials and Lie theory. Our starting point will be the classical Capelli operator, a mysterious element of the enveloping algebra $U(gl(n,C))$ that was discovered in the 19th century. We will then see how representation theory can be used to generalize the Capelli operators to other interesting families of operators and their associated n-variable polynomials, such as Knop-Sahi, Okounkov-Olshanski, and Sergeev-Veselov polynomials.

The mini-course will be accessible to graduate students. It is tuned for anyone interested in algebra or algebraic combinatorics.