Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Infinite rank module categories over finite dimensional $\mathfrak{sl}_2$-modules in Lie-algebraic context (2405.19894v1)

Published 30 May 2024 in math.RT

Abstract: We study locally finitary realizations of simple transitive module categories of infinite rank over the monoidal category $\mathscr{C}$ of finite dimensional modules for the complex Lie algebra $\mathfrak{sl}2$. Combinatorics of such realizations is governed by six infinite Coxeter diagrams. We show that five of these are realizable in our setup, while one (type $B\infty$) is not. We also describe the $\mathscr{C}$-module subcategories of $\mathfrak{sl}_2$-mod generated by simple modules as well as the $\mathscr{C}$-module categories coming from the natural action of $\mathscr{C}$ on the categories of finite dimensional modules over Lie subalgebras of $\mathfrak{sl}_2$.

Summary

We haven't generated a summary for this paper yet.