Moderator:
Malihe Yousofzadeh (ma.yousofzadeh@sci.ui.ac.ir)
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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.
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