Motives of central slope Kronecker moduli

We use dualities of quiver moduli induced by reflection functors to describe generating series of motives of Kronecker moduli spaces of central slope as solutions of algebraic and q-difference equations.

💡 Research Summary

The paper “Motives of central slope Kronecker moduli” studies the motivic invariants of framed Kronecker moduli spaces at the special value of the stability parameter known as the central slope. The authors exploit the rich symmetry coming from reflection functors in quiver representation theory to obtain dualities between moduli spaces, and they translate these geometric dualities into precise identities for generating series of virtual motives.

The work begins with a concise review of quiver representation theory, stability conditions (both Θ‑stability and slope μ‑stability), and the construction of GIT quotients M_Θ^{sst}(d) for a given dimension vector d. Lemma 2.2 establishes that reversing all arrows of a quiver (the opposite quiver) and changing the sign of the stability functional yields an isomorphic moduli space, a fact that underlies the later dualities.

Motivic considerations are carried out in the localized Grothendieck ring R = K₀(Var_ℂ)