Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras

Hiraku Nakajima (Kavli IPMU, Tokyo, Japan)

02-Jul-2020, 12:00-13:00 (4 years ago)

Abstract: Balazs explained his conjecture with Gyenge and Nemethi on Euler numbers of Hilbert schemes on June 4. I proved it by showing that quantum dimensions of standard modules of quantum affine algebras are always 1. This remarkable property is the simplest case of a conjecture on quantum dimensions of Kirillov-Reshetikhin modules proposed by Kuniba in 93, which is still open for E7,8 in general. In this talk, I will emphasize on representation theoretic aspects to minimize overlaps with Balazs' talk.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )


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