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Seminar by R Biswal (over Skype)

Friday, May 8, 2020 - 15:00 to 16:00
Conference Room, School of Mathematical Sciences
Rekha Biswal
Max Planck Institute for Mathematics, Bonn
Macdonald polynomials and level two Demazure modules for affine sl_{n+1}

An important result due to Sanderson and Ion says that characters of level one Demazure modules are Macdonald polynomials specialized at t=0. In this talk,
I will introduce a new class of symmetric polynomials expressed as linear combination of Macdonald polynomials. Using representation theory, we will see that these new class of polynomials are graded characters of an interesting class of modules of the current algebra $sl_{n+1}[t]$, interpolate between characters of level one and level two Demazure modules and gives rise to new results in representation theory of current algebras as a corollary.

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