Hexagon

hexagon:2610.00403v1

math.RT — Representation Theory

Hall polynomials for representation-finite algebras

Contributed by Qiyue Tang

We prove the Hall polynomial existence conjecture for representation-finite algebras over finite fields.

A mix of human-written and AI-generated textHuman understanding: some partsHall polynomial

Oct 20, 2026PDF ↗View work →

hexagon:2610.00392v2

math.RT — Representation Theory

Cartan determinants in finite representation type over arbitrary fields

Contributed by Qiyue Tang

Let $A$ be a finite-dimensional representation-finite algebra over an arbitrary field, and let $M$ be a nonzero finite-dimensional right $A$ -module. We prove that $\operatorname{End}_A(M)$ has Cartan determinant one whenever it has finite global dimension. In particular, the Cartan determinant conjecture holds for representation-finite algebras over arbitrary fields.

A mix of human-written and AI-generated textHuman understanding: some partsCartan determinant

Oct 20, 2026PDF ↗View work →

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Hall polynomials for representation-finite algebras

Cartan determinants in finite representation type over arbitrary fields

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