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Results tagged with rt.representation-theory
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user 62601
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
3
votes
1
answer
145
views
Does the Leclerc-Thibon involution exchange vertex operators of the first and second type?
This question is about $U_q ( \hat{\mathfrak{sl}}_2 )$ representation theory. There is a notion of vertex operators $\Phi_{\pm }(z)$ of first and $\Psi_{\pm}(z)$ of the second type. They are defined …
- 385
1
vote
Accepted
Does the Leclerc-Thibon involution exchange vertex operators of the first and second type?
I found the answer to the first question. Second and third questions remain.
\begin{align}
\Phi_+ (z) \rightarrow K^{-1/2} \Psi_+ (q^{-1} z) \\
\Phi_- (z) \rightarrow K^{1/2} \Psi_- (q^{-1} z)
\end{a …
- 385
3
votes
1
answer
475
views
Harish-Chandra isomorphism for characteristic $p$
I am trying to understand the proof of Theorem 1 from this paper V. Kac and B. Weisfeiler (Indag. Math. 1976, DOI link).
Theorem 1. Let either $p\neq 2$ or $\varrho\in X(\mathscr{T})$. Then $\gamm …
- 385