The support conjecture for rank-two quantum triangular bases

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.RA — Rings and Algebrasmath.RT — Representation Theory

Contributed by 琪越 唐 ↗

Submitter琪越 唐

Version 1 / Sep 30, 2026 / CC BY 4.0

Abstract

We prove Conjecture 11 of Lee, Li, Rupel, and Zelevinsky on the support of triangular basis elements in rank-two quantum cluster algebras.

Provenance statement

The main results of this paper were generated using GPT-6-Astra and verified by the Danus system.

References

  1. A. Berenstein and A. Zelevinsky, Triangular bases in quantum cluster algebras , Int. Math. Res. Not. IMRN 2014 (2014), no. 6, 1651--1688. https://arxiv.org/abs/1206.3586 arXiv:1206.3586 ; version 2.arXiv
  2. M. A. de Cataldo and L. Migliorini, The decomposition theorem, perverse sheaves and the topology of algebraic maps , Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 4, 535--633. https://arxiv.org/abs/0712.0349v2 arXiv:0712.0349 ; version 2.arXiv
  3. K. Lee, L. Li, D. Rupel, and A. Zelevinsky, Greedy bases in rank 2 quantum cluster algebras , Proc. Natl. Acad. Sci. USA 111 (2014), no. 27, 9712--9716. https://arxiv.org/abs/1405.2311 arXiv:1405.2311 ; version 1.arXiv
  4. L. Li, Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras , J. Algebra 634 (2023), 97--164. https://arxiv.org/abs/2208.12307 arXiv:2208.12307 ; version 2.arXiv
  5. L. Li, Nakajima's quiver varieties and triangular bases of bipartite cluster algebras , in Representation Theory and Flag Varieties , Contemp. Math. 837 (2026), 131--158. https://arxiv.org/abs/2405.08234 arXiv:2405.08234 . The result numbering used here refers to version 1 of the preprint.arXiv

Version history

  1. v1Initial depositCurrentSep 30, 2026