Grothendieck classes of quiver varieties

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Abstract

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. Our formula is stated in terms of coefficients that are uniquely determined by the geometry and can be computed by an explicit combinatorial algorithm. We conjecture that these coefficients have signs that alternate with degree. The proof of our formula involves K-theoretic generalizations of several useful cohomological tools, including the Thom-Porteous formula, the Jacobi-Trudi formula, and a Gysin formula of P. Pragacz.

Original languageEnglish (US)
Pages (from-to)75-103
Number of pages29
JournalDuke Mathematical Journal
Volume115
Issue number1
DOIs
StatePublished - Oct 1 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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