Wakimoto modules for the affine Lie superalgebras A(m−1, n−1)(1) and D(2, 1, a)(1)

2002 ◽  
Vol 132 (3) ◽  
pp. 419-433 ◽  
Author(s):  
KENJI IOHARA ◽  
YOSHIYUKI KOGA
Keyword(s):  
Critical Level ◽  
Lie Superalgebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Basic Affine ◽  
Weight Modules

In this paper, we construct Wakimoto modules for basic affine Lie superalgebras of type A(m−1, n−1)(1) and D(2, 1, a)(1). As an application, we compute the characters of irreducible highest weight modules at the critical level.

scholarly journals Factorization of the canonical bases for higher-level Fock spaces

2011 ◽  
Vol 55 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Susumu Ariki ◽  
Nicolas Jacon ◽  
Cédric Lecouvey
Keyword(s):  
Fock Space ◽  
Fock Spaces ◽  
Transition Matrices ◽  
Canonical Bases ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Graphic Module ◽  
Module Structures ◽  
Weight Modules

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.

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