Naslov
On principal realization of modules for the affine Lie algebra $A_1 ^{;;; ; ; (1)};;; ; ; $ at the critical level

Autori
Adamović, Dražen ; Jing, Naihuan ; Misra, Kailash C.

Izvornik
Transactions of the American mathematical society (0002-9947) 369 (2017), 7; 5113-5136

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
es. Vertex superalgebras ; affine Lie algebras ; Clifford algebras ; Weyl algebra ; lattice vertex operator algebras ; critical level ; Z-algebras
(es. Vertex superalgebras ; affine Lie algebras ; Clifford algebras ; Weyl algebra ; lattice vertex operator algebras ; critical level ; Z-algebras.)

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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