تقرير
Classification of charge-conserving loop braid representations
| العنوان: | Classification of charge-conserving loop braid representations |
|---|---|
| المؤلفون: | Martin, Paul, Rowell, Eric C., Torzewska, Fiona |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematics - Representation Theory, 16T25, 20F36, 18M05 |
| الوصف: | Here a loop braid representation is a monoidal functor $\mathsf{F}$ from the loop braid category $\mathsf{L}$ to a suitable target category, and is $N$-charge-conserving if that target is the category $\mathsf{Match}^N$ of charge-conserving matrices (specifically $\mathsf{Match}^N$ is the same rank-$N$ charge-conserving monoidal subcategory of the monoidal category $\mathsf{Mat}$ used to classify braid representations in arXiv:2112.04533) with $\mathsf{F}$ strict, and surjective on $\mathbb{N}$, the object monoid. We classify and construct all such representations. In particular we prove that representations fall into varieties indexed by a set in bijection with the set of pairs of plane partitions of total degree $N$. Comment: 38 pages, 7 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2301.13831 |
| رقم الأكسشن: | edsarx.2301.13831 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |