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Results tagged with qa.quantum-algebra
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user 4231
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
4
votes
Indecomposable, non-simple, modules of quantum groups at roots of unity
In the case of the rank 1 simple Lie algebra, your references give a good account of what is known. But in general, it's wise to keep in mind that many of the indecomposable $U_q(\mathfrak{g})$-mod …
- 52.9k
12
votes
1
answer
681
views
Comparing a Chevalley basis with the canonical basis of the adjoint module?
First some background: Given a simple Lie algebra $\mathfrak{g}$ over an algebraically closed field of characteristic 0 such as $\mathbb{C}$, fix a Cartan decomposition $\mathfrak{g} = \mathfrak{h} \o …
CommunityBot
- 1
5
votes
expository papers related to quantum groups
This is mostly meant as a reminder that the original question asks about articles and not books or research papers. Of the latter there are a huge number by now. The notion of "quantum group" has …
- 52.9k
8
votes
Accepted
Kazhdan Lusztig Map and conjugacy classes of Weyl groups.
The question itself is not precisely enough stated (or documented) to permit a real answer, I think. It's an old problem to specify some "natural" correspondence between conjugacy classes in a Weyl …
- 52.9k
8
votes
Is there a fusion rule in positive characteristic?
To answer the question in the header, there is certainly a relevant fusion rule in positive characteristic. This arises in a purely representation-theoretic context in the work of various people (Ol …
- 52.9k
13
votes
Accepted
Traces on Hecke algebras and the Jones polynomial
The answer to both questions is positive (since mathematicians tend to leave no stone unturned). See for example:
Geck, Meinolf; Lambropoulou, Sofia. Markov traces and knot invariants related to Iw …
- 52.9k
9
votes
Accepted
Simple modules for $U_q(\mathfrak{sl}_n)$ at roots of unity
I'm interpreting your quantum group as the quantized enveloping algebra studied by Lusztig and many others, starting with the divided power version of the usual enveloping algebra of a semisimple Lie …
- 52.9k