Canonical bases and higher representation theory

Author:

Webster Ben

Abstract

AbstractThis paper develops a general theory of canonical bases and how they arise naturally in the context of categorification. As an application, we show that Lusztig’s canonical basis in the whole quantized universal enveloping algebra is given by the classes of the indecomposable 1-morphisms in a categorification when the associated Lie algebra is of finite type and simply laced. We also introduce natural categories whose Grothendieck groups correspond to the tensor products of lowest- and highest-weight integrable representations. This generalizes past work of the author’s in the highest-weight case.

Publisher

Wiley

Subject

Algebra and Number Theory

Reference44 articles.

1. [Web13a] B. Webster , Knot invariants and higher representation theory, Preprint (2013), arXiv:1309.3796.

2. [Web12b] B. Webster , Weighted Khovanov–Lauda–Rouquier algebras, Preprint (2012), arXiv:1209.2463.

3. [Web12a] B. Webster , A categorical action on quantized quiver varieties, Preprint (2012), arXiv:1208.5957.

4. [TW12] P. Tingley and B. Webster , Mirković–Vilonen polytopes and Khovanov–Lauda–Rouquier algebras, Preprint (2012), arXiv:1210.6921.

5. [Sus08] J. Sussan , Positivity and the canonical basis of tensor products of finite-dimensional irreducible representations of quantum  $\mathfrak{sl}(k)$ , Preprint (2008), arXiv:0804.2034.

Cited by 35 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Gelfand-Tsetlin Modules: Canonicity and Calculations;Algebras and Representation Theory;2024-03-27

2. Semi-Infinite Highest Weight Categories;Memoirs of the American Mathematical Society;2024-01

3. Rational Cherednik algebras of G(ℓ,p,n) from the Coulomb perspective;Advances in Mathematics;2023-11

4. Representations of cyclotomic oriented Brauer categories;Journal of Pure and Applied Algebra;2023-06

5. Trace Decategorification of Categorified Quantum sl(3);Applied Categorical Structures;2023-01-11

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3