Napredna pretraga

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

Adamović, Dražen; Jing, Naihuan; Misra, Kailash C.
On principal realization of modules for the affine Lie algebra $A_1 ^{; ; ; (1)}; ; ;$ at the critical level // Transactions of the American Mathematical Society, 369 (2017), 7; 5113-5136 doi:10.1090/tran/7009 (međunarodna recenzija, članak, znanstveni)

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

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

Projekt / tema
HRZZ-IP-2013-11-2634 - Algebarske i kombinatorne metode u teoriji verteks algebri (Dražen Adamović, )
ZCI QuantiXLie

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem: