Hall polynomials for tame quivers with automorphism (Q2075244)

Classical Hall polynomials play important roles in the study of representations of symmetric groups and general linear groups. They are defined by counting certain subgroups of finite abelian \(p\)-groups, which are closely connected to Hall-Littlewood functions. Let \(Q\) be a tame quiver with automorphism \(\sigma\). The pair \((Q,\sigma)\) defines a family of tame hereditary algebras \(\mathfrak{U}(Q,\sigma;q)\) over a finite field \(\mathbb{F}_q\) of \(q\) elements. The authors prove that Hall polynomial exists for each triple of decomposition sequences associated with tame quivers with automorphism \(\mathfrak{U}(Q,\sigma;q)\) (Theorem 3.6, page 228).