Counting Representations of Quivers over Finite Fields

By Jiuzhao Hua. 2000

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The integrality conjecture and the cohomology of preprojective stacks (2016, methodology): “The weight series of the mixed Hodge structures (2) are described in terms of the Kac polynomials [23] of Q, via the results of [21] and [32], and so Theorem A enables us to calculate the compactly supported cohomology Hc(M(ΠQ)d,Q) itself.”
Absolutely indecomposable representations and Kac-Moody Lie algebras (2001, unknown): “R A ] 1 9”
Kac’s conjecture from Nakajima quiver varieties (2008, methodology): “In the special case of x = 0 [14, Theorem 10.2] implies: Theorem 11 (Nakajima) Fix w ∈ NI then ∑ v∈NI dim ( H2dv,w (M(v,w) ) Xv = ∑ α∈NI dim ( L(Λw)Λw−α ) Xα (29) We notice that the denominator of the RHS of (1) agrees with the LHS of Hua’s (26).”
Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, I (2015, background): “[Hua00] J. Hua, Counting representations of quivers over finite fields, J. Algebra 226 (2000), no. 2, 1011–1033.”
Arithmetic harmonic analysis on character and quiver varieties II (2008, methodology): “It is based on Hua’s formula [13] for the number of absolutely indecomposable representations of quivers over finite fields.”