Nakajima's quiver varieties and triangular bases of rank-2 cluster algebras

نویسندگان

چکیده

Berenstein and Zelevinsky introduced quantum cluster algebras [3] the triangular bases [4]. The support conjecture in [12] asserts that of a basis element for rank-2 algebra is bounded by an explicitly described region possibly concave. In this paper, we prove all skew-symmetric algebras.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quiver Varieties and Cluster Algebras

Motivated by a recent conjecture by Hernandez and Leclerc [30], we embed a Fomin-Zelevinsky cluster algebra [20] into the Grothendieck ring R of the category of representations of quantum loop algebras Uq(Lg) of a symmetric Kac-Moody Lie algebra, studied earlier by the author via perverse sheaves on graded quiver varieties [48]. Graded quiver varieties controlling the image can be identified wi...

متن کامل

Triangular Bases in Quantum Cluster Algebras

A lot of recent activity has been directed toward various constructions of “natural” bases in cluster algebras. We develop a new approach to this problem which is close in spirit to Lusztig’s construction of a canonical basis, and the pioneering construction of the Kazhdan–Lusztig basis in a Hecke algebra. The key ingredient of our approach is a new version of Lusztig’s Lemma that we apply to a...

متن کامل

Greedy bases in rank 2 quantum cluster algebras.

We identify a quantum lift of the greedy basis for rank 2 coefficient-free cluster algebras. Our main result is that our construction does not depend on the choice of initial cluster, that it builds all cluster monomials, and that it produces bar-invariant elements. We also present several conjectures related to this quantum greedy basis and the triangular basis of Berenstein and Zelevinsky.

متن کامل

Cluster Algebras and Quiver Representations

These notes contain an extended abstract and references for a minicourse given at the Summer School ‘Microlocal and Geometric Methods in Representation Theory’ (Schloss Reisensburg, July 2006) of the International Research Training Group Metz–Paderborn.

متن کامل

Handsaw Quiver Varieties and Finite W -algebras

Following Braverman–Finkelberg–Feigin–Rybnikov (arXiv: 1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W -algebra of type A. This is a finite analog of the AGT conjecture on 4-dimensional supersymmetric Yang–Mills theory with surface operators. Our new observation is that the C-fixed point set of a handsaw quiver variety is...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2023

ISSN: ['1090-266X', '0021-8693']

DOI: https://doi.org/10.1016/j.jalgebra.2023.06.028