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Results tagged with qa.quantum-algebra
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user 4366
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
4
votes
Simple modules for $U_q(\mathfrak{sl}_n)$ at roots of unity
Look at the paper Quantum Affine Algebras at Roots of Unity of Chari and Pressley (published as https://doi.org/10.1090/S1088-4165-97-00030-7).
- 1,472
4
votes
Practical Ways to get Skew-Schur Functions
As this is a representation theory question, the connection to affine Hecke algebras deserves a few more words. The (degenerate) affine Hecke algebra, $H_d$ is isomorphic as a vector space to $\mathbb …
- 1,472
1
vote
Accepted
classification of irreducible finite dimensional representation of affine hecke algebra of t...
This is done in Orellana-Ram, `Affine braids, Markov Traces and the category O'. The answer is essentially the same as for the degenerate affine Hecke algebra.
- 1,472
2
votes
1
answer
227
views
A question on Lusztig's `graph with automorphism' construction?
Using the notion of a graph with compatible automorphism, Lusztig constructs all symmetrizable Cartan data (i.e. Cartan matrices $A$ for which there is a diagonal matrix $D=\mathrm{diag}(d_1,\ldots,d_ …
- 1,472
3
votes
Does some version of U_q(gl(1|1)) have a basis like Lusztig's basis for \dot{U(sl_2)}?
Kashiwara has developed some crystal theoretic methods for the Lie superalgebra $\mathfrak{q}(n)$. However, I think you should look at Khovanov, to get an idea of what it should look like.
- 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 …
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