Grothendieck classes of quiver varieties
By Anders Skovsted Buch. 2001
64 citations recorded by the source corpus.
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. We furthermore conjecture that the coefficients in our formula have signs which 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 Pragacz.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f5e44cae4292def7ce7154d55e2727050f562650
How researchers see this paper
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In Discrete Mathematics and Combinatorics
- Alexander Yong
- Hugh Thomas
- Ezra Miller
- Anders Skovsted Buch
- Mikhail Kogan
- Matthew J. Samuel
- N. Perrin
- David Anderson
In Geometry and Topology
- Alexander Yong
- Hugh Thomas
- Ezra Miller
- Mikhail Kogan
- Anders Skovsted Buch
- Allen Knutson
- David Anderson
- I. Reiten
Citations in the corpus
- A Littlewood-Richardson rule for theK-theory of Grassmannians (2000, methodology): “The coefficients ~w~ also generalize the structure constants c~ and d~ of F. On the other hand, the coefficients ~w~ are special cases of quiver coefficients c~(~) which will be introduced in [ 2 ].”
- Four positive formulae for type A quiver polynomials (2003, unknown): “It implies Buch’s conjecture [ Buc02 ] that the K-theoretic analogues of the quiver constants c (r) exhibit a certain sign alternation, generalizing the positivity of c (r).”
- Toric degeneration of Schubert varieties and Gelfand¿Tsetlin polytopes (2003, background): “Indeed, this is what geometrically produces (or reproduces) various combinatorial formulae (for classical objects such as Littlewood–Richardson coefficients [Ful97], or for universally defined polynomials discovered more recently [LS82a, LS82b, Ful99, BF99 , Buc02]): components of the special fiber”
- A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (2007, background): “2006], which is a problem that has remained open in this topic; see [Buch 2002a; 2005a].”