Multiplicative structure of the K-theoretic McKay correspondence for Hilbert scheme of points

Speaker(s)

Jakub Koncki

Affiliation

IMPAN/UW

Date

Jan. 8, 2024, 10:30 a.m.

Room

room 4070

Seminar

Seminar Algebraic Topology

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Hilbert scheme of points in a complex plane  is a classical object of study in algebraic geometry. McKay correspondence provides an isomorphism of vector spaces between its K-theory (or cohomology) and the space of symmetric functions, creating a bridge between geometry and combinatorics. Multiplication by a class in the K-theory induces an endomorphism of the space of symmetric functions.

In the cohomology case, compact formulas for such maps were found by Lehn and Sorger.  The K-theoretical case was studied by Boissière using torus equivariant techniques. He proved a formula for multiplication by the class of tautological bundle and stated a conjecture for remaining generators of the K-theory of Hilbert scheme.  In the talk I will show how torus action simplifies the problem and prove the conjectured formula using restriction to a one-dimensional subtorus.

This is a joint project with M. Zielenkiewicz.

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