On principal realization of modules for the affine Lie algebra $A_1 ^{;;; ; ; (1)};;; ; ; $ at the critical level (CROSBI ID 237139)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Adamović, Dražen ; Jing, Naihuan ; Misra, Kailash C.
engleski
On principal realization of modules for the affine Lie algebra $A_1 ^{;;; ; ; (1)};;; ; ; $ at the critical level
We present complete realization of irreducible $A_1 ^{; ; ; ; ; (1)}; ; ; ; ; $-- modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z- algebra approach to this construction. All irreducible highest weight $A_1 ^{; ; ; ; ; (1)}; ; ; ; ; $--modules at the critical level are realized on the vector space $M_{; ; ; ; ; \tfrac{; ; ; ; ; 1}; ; ; ; ; {; ; ; ; ; 2}; ; ; ; ; + \Z}; ; ; ; ; (1) ^{; ; ; ; ; \otimes 2}; ; ; ; ; $ where $M_{; ; ; ; ; \tfrac{; ; ; ; ; 1}; ; ; ; ; {; ; ; ; ; 2}; ; ; ; ; + \Z}; ; ; ; ; (1) $ is the polynomial ring ${; ; ; ; ; \C}; ; ; ; ; [\alpha(-1/2), \alpha(-3/2), ...]$. Explicit combinatorial bases for these modules are also given.
es. Vertex superalgebras ; affine Lie algebras ; Clifford algebras ; Weyl algebra ; lattice vertex operator algebras ; critical level ; Z-algebras.
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Podaci o izdanju
369 (7)
2017.
5113-5136
objavljeno
0002-9947
1088-6850
10.1090/tran/7009