Twisted Localization of Weight Modules

Author(s):  
Dimitar Grantcharov
Keyword(s):  
2004 ◽  
Vol 356 (8) ◽  
pp. 3403-3404 ◽  
Author(s):  
Ivan Dimitrov ◽  
Olivier Mathieu ◽  
Ivan Penkov
Keyword(s):  

2015 ◽  
Vol 219 (8) ◽  
pp. 3427-3444 ◽  
Author(s):  
Rencai Lü ◽  
Volodymyr Mazorchuk ◽  
Kaiming Zhao

2011 ◽  
Vol 55 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Susumu Ariki ◽  
Nicolas Jacon ◽  
Cédric Lecouvey

AbstractThe level l Fock space admits canonical bases $\mathcal{G}_{e}$ and $\smash{\mathcal{G}_{\infty}}$. They correspond to $\smash{\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})}$ and $\mathcal{U}_{v}({\mathfrak{sl}}_{\infty})$-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.


2020 ◽  
Vol 25 (4) ◽  
pp. 1125-1160
Author(s):  
DIMITAR GRANTCHAROV ◽  
IVAN PENKOV
Keyword(s):  

Abstract We classify the simple bounded weight modules of the Lie algebras $$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right) $$ sl ∞ , o ∞ and $$ \mathfrak{sp}\left(\infty \right) $$ sp ∞ , and compute their annihilators in $$ U\left(\mathfrak{sl}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{o}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{sp}\left(\infty \right)\right) $$ U sl ∞ , U o ∞ , U sp ∞ , respectively.


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