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

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

1998 ◽  
Vol 39 (5) ◽  
pp. 2910-2928 ◽  
Author(s):  
Carina Boyallian ◽  
Victor G. Kac ◽  
José I. Liberati ◽  
Catherine H. Yan
Keyword(s):  
Lie Algebra ◽  
Differential Operators ◽  
Highest Weight ◽  
Matrix Differential Operators ◽  
Highest Weight Modules ◽  
Matrix Differential ◽  
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.

Highest weight modules over the Lie algebra g(A)

1983 ◽  
pp. 103-118 ◽  
Author(s):  
Victor G. Kac
Keyword(s):  
Lie Algebra ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

scholarly journals Classifying Relaxed Highest-Weight Modules for Admissible-Level Bershadsky–Polyakov Algebras

2021 ◽  
Author(s):  
Zachary Fehily ◽  
Kazuya Kawasetsu ◽  
David Ridout
Keyword(s):  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

scholarly journals Unitarizable highest weight modules of the conformal group

1982 ◽  
Vol 45 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Floyd L. Williams
Keyword(s):  
Conformal Group ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

Categories of nonstandard highest weight modules for affine Lie algebras

1996 ◽  
Vol 221 (1) ◽  
pp. 193-209 ◽  
Author(s):  
B. Cox ◽  
V. Futorny ◽  
D. Melville
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

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.

Whittaker modules associated with highest weight modules

1990 ◽  
Vol 60 (1) ◽  
pp. 59-113 ◽  
Author(s):  
Hisayosi Matumoto
Keyword(s):  
Highest Weight ◽  
Highest Weight Modules ◽  
Whittaker Modules ◽  
Weight Modules
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