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Tagged with modular-tensor-categories quantum-groups
7 questions
4
votes
0
answers
95
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Ribbon fusion categories for quantum $\mathfrak{sl}_2$ at odd roots of unity
I will work over $\mathbb{C}$. Let $q=e^{2\pi i/N}$, and write $U_{q}(\mathfrak{sl}_2)$ for Lusztig's divided power quantum group for $\mathfrak{sl}_2$.
One can associate to $U_{q}(\mathfrak{sl}_2)$ a ...
3
votes
2
answers
113
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Does unitarity and modularity constrain fusion multiplicities to be 0,1?
If I have a braided tensor category that's unitary and modular, then how does the unitarity and modularity constrain the fusion multiplicities?
I know that if $a,b,c \in ob({C})$ satisfy the fusion ...
- 569
2
votes
1
answer
216
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Relation between the modular categories SU(2)_n and Sp(n)_1
The online database [1] provides a list of some modular tensor categories classified by rank. Let us consider the two modular categories denoted kmA1_$\ell$ and kmC$\ell$_1 (i.e. Kac Moody $A_1$ level ...
3
votes
0
answers
148
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Symmetries of modular categories coming from quantum groups
This is a request for references about the computation of the braided autoequivalences of fusion categories coming from a quantum group. I could not find even the description of braided ...
- 1,529
7
votes
2
answers
623
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How to make a premodular category a modular tensor category?
A premodular category (also called ribbon fusion category) is roughly speaking a tensor category where fusion and braiding of the objects are defined. With an extra nondegeneracy condition for the ...
- 875
20
votes
1
answer
962
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Is the representation category of quantum groups at root of unity visibly unitary?
Let $\mathfrak g$ be a simple Lie algebra.
By taking the specialization at $q^\ell=1$ of a certain integral version¹ of the quantum group $U_q(\mathfrak g)$,
and by considering a certain quotient ...
- 43.2k
4
votes
3
answers
473
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What's the best reference for actual formulas for RT invariants?
If one really wants to understand the formulas for how to construct the Reshetikhin-Turaev 3-manifold invariants coming from quantum groups in terms of R-matrices and such, what's the best reference ...
- 44.7k