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Nov 7, 2023 at 20:35 vote accept Student
Nov 6, 2023 at 17:28 comment added Sachin Valera @Student I don't know of any references RE unitary representations of $H_{n}(Q,k)$ in unitary braided fusion categories (although someone else might...), so drafted some rough(!!) notes (see edit above). If you end up reading any of this and something's unclear, you're welcome to ask.
Nov 6, 2023 at 17:22 history edited Sachin Valera CC BY-SA 4.0
1. Clarified trace on morphism, 2. Attached link to notes in response to OPs comment
Oct 29, 2023 at 11:45 comment added Student This is eye-opening. Could you please provide some more justification (or at least some reference) for that $End(q^{\otimes n})$ provides a unitary representation of $H_n(Q,k)$? Another question - while $H_n(Q,2)$ is ubiquitous in math, do the higher generalised Iwahori-Hecke algebras $H_n(Q,k)$ show up in some other fields in mathematics?!
Oct 28, 2023 at 20:02 history answered Sachin Valera CC BY-SA 4.0