scholarly journals Quasifinite highest weight modules over the Lie algebra of differential operators on the circle

1993 ◽  
Vol 157 (3) ◽  
pp. 429-457 ◽  
Author(s):  
Victor Kac ◽  
Andrey Radul
Keyword(s):  
Lie Algebra ◽  
Differential Operators ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

scholarly journals Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero

2003 ◽  
Vol 46 (4) ◽  
pp. 529-537 ◽  
Author(s):  
Yuly Billig
Keyword(s):  
Lie Algebra ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Highest Weight ◽  
Level Zero ◽  
Maximal Submodule ◽  
Highest Weight Modules ◽  
Weight Modules

AbstractWe describe the structure of the irreducible highest weight modules for the twisted Heisenberg–Virasoro Lie algebra at level zero. We prove that either a Verma module is irreducible or its maximal submodule is cyclic.

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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