The Representation Theory of Brauer Categories I: Triangular Categories
- Award ID(s):
- 1849173
- PAR ID:
- 10472608
- Publisher / Repository:
- arxiv
- Date Published:
- Journal Name:
- Applied Categorical Structures
- Volume:
- 30
- Issue:
- 6
- ISSN:
- 0927-2852
- Page Range / eLocation ID:
- 1203 to 1256
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Generalized Temperley–Lieb–Jones (TLJ) 2-categories associated to weighted bidirected graphs were introduced in unpublished work of Morrison and Walker. We introduce unitary modules for these generalized TLJ 2-categories as strong ∗-pseudofunctors into the ∗-2-category of row-finite separable bigraded Hilbert spaces. We classify these modules up to ∗-equivalence in terms of weighted bi-directed fair and balanced graphs in the spirit of Yamagami’s classification of fiber functors on TLJ categories and DeCommer and Yamashita’s classification of unitary modules for [Formula: see text].more » « less
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