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Results tagged with quantum-groups
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user 4366
Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.
5
votes
1
answer
683
views
Convex PBW bases
Given a reduced expression for the longest word $w_0$ in the Weyl group of $\mathfrak{g}=\mathfrak{n}^+\oplus\mathfrak{h}\oplus{n}^-$, one obtains a convex ordering on the set of positive roots, $\be …
- 1,472
5
votes
Accepted
notation in Lusztig's book: introduction to quantum groups
Yes, the $E$, $F$, and $K$ are standard generators of $U_\nu(\mathfrak{sl}_2)$. Sometimes $$q=\nu^{-1}.$$
I don't know what is standard. More generally, the standard (Chevalley) generators for $U_\nu$ …
- 1,472
3
votes
When does Lusztig's canonical basis have non-positive structure coefficients?
Ben,
I have heard the same thing, but I have never seen an example. After thinking about it a bit, I came up with the following 'heuristic' reason why the structure constants should be positive for ha …
- 1,472