在Heisenberg范畴中嵌入Deligne的范畴$\ mathm {\Underline{Re}p}(S_t)$

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2019-05-14 DOI:10.4171/QT/147

Samuel Nyobe Likeng, Alistair Savage

引用次数: 0

摘要

我们定义了一个忠实的线性一元函子，从划分范畴，从而从Deligne的范畴Rep(St)，到海森堡范畴的加性Karoubi包络。我们证明了Grothendieck环上的诱导映射是内射的，并且对应于对称函数上的Kronecker副积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Embedding Deligne's category $\mathrm{\Underline{Re}p}(S_t)$ in the Heisenberg category

We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category Rep(St), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.