All Questions
7 questions
5
votes
1
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600
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exceptional cases in Kazhdan-Lusztig
The Kazhdan-Lusztig story doesn't apply to the four exceptional cases $(E_6)_1$, $(E_7)_1$, $(E_8)_1$, $(E_8)_2$ (see this earlier question of mine).
What's special about those cases?
- 43.2k
3
votes
0
answers
107
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How to get $U(N)_k$ Kac-Moody modules and characters from $N \cdot k$ Dirac Fermions using $U(N \cdot k)_1 / SU(k)_N$?
It is known that the $U(N)_k$ Kac-Moody algebra can be written as the coset $U(N)_k = U(N \cdot k)_1 / SU(k)_N$. (This fact is related to the level-rank duality of $U(N)_k \leftrightarrow U(k)_N$.) A ...
- 545
3
votes
0
answers
91
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Hopf algebras structure and quantum affine algebras
I'm looking for some information about the Hopf algebras structure and the quantum groups.
In particularly I was wondering if (and eventually where) is defined in the case of quantum affine algebras ...
- 31
2
votes
1
answer
176
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How does an element $T\left(z\right)$ act on a $\mathcal{U}_{q}\left(\mathcal{L}\mathfrak{sl}_{2}\right)\left[\left[z\right]\right]$-module?
Context
Let $V$ be a 2-dimensional evaluation representation of the quantum loop algebra $\mathcal{U}_{q}\left(\mathcal{L}\mathfrak{sl}_{2}\right)$ with $a=q$. Also, for $m\in\mathbb{Z}$, the ...
- 357
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 ...
2
votes
0
answers
132
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A question about q-binomials at roots of unity
I have a question about a lemma $9.3.6$ in the book A Guide to Quantum Groups written by Vyjayanthi Chari and Andrew Pressley. This question comes from page 301, "The restricted specialization&...
- 137
1
vote
1
answer
64
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What is $\left[ \begin{array}{c} K_i;0\\ \ell\\ \end{array} \right] _{\varepsilon _i}$ in the restricted specialization in QUE algebras?
I have a question about the book A Guide to Quantum Groups written by Vyjayanthi Chari and Andrew Pressley. It comes from section $9.3$ on page $300$ of this book
In Section 9.1, the authors define ...
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