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Motives of Nullcones of Quiver Representations

Lydia Gösmann, Markus Reineke

Abstract

We derive two formulas for motives of nullcones of quiver representations, one being explicit, the other being of wall-crossing type.

Motives of Nullcones of Quiver Representations

Abstract

We derive two formulas for motives of nullcones of quiver representations, one being explicit, the other being of wall-crossing type.

Paper Structure

This paper contains 12 sections, 19 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. An explicit recursive formula for the motive of the nullcone
  3. Quiver representations and their nullcone
  4. Motives
  5. The recursive formula
  6. Applications and examples
  7. Applications
  8. Examples
  9. Hesselink stratification and rational/integral level quiver
  10. Introduction
  11. Rational/integral level quiver
  12. Wall-crossing type formula

Key Result

Theorem 2.1

The following are equivalent for a representation $V\in R_\mathbf{d}$:

Theorems & Definitions (32)

  • Theorem 2.1: LB
  • Theorem 2.2
  • Corollary 3.1
  • Corollary 3.2
  • Corollary 3.3
  • Corollary 3.4
  • Corollary 3.5
  • Remark 3.6
  • Definition 4.1
  • Remark 4.2: see LB
  • ...and 22 more