Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated...
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| Other Authors: | , , |
| Format: | article |
| Language: | eng |
| Published: |
2021
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.1/15114 |
| Country: | Portugal |
| Oai: | oai:sapientia.ualg.pt:10400.1/15114 |
| Summary: | The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4. |
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