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Whittaker modules for the affine Lie algebra A_1 ^(1)


Adamović, Dražen; Lu, Rencai; Zhao, Kaiming
Whittaker modules for the affine Lie algebra A_1 ^(1) // Advances in mathematics, 289 (2016), 438-479 doi:10.1016/j.aim.2015.11.020 (međunarodna recenzija, članak, znanstveni)


Naslov
Whittaker modules for the affine Lie algebra A_1 ^(1)

Autori
Adamović, Dražen ; Lu, Rencai ; Zhao, Kaiming

Izvornik
Advances in mathematics (0001-8708) 289 (2016); 438-479

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

Ključne riječi
Wakimoto modules; Whittaker modules; affine Lie algebra; vertex algebra; critical level

Sažetak
We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra $\widehat{; ; ; sl_2}; ; ; $ of type $A_1^{; ; ; (1)}; ; ; $ with noncritical level. These modules can become simple Whittaker modules over $\widetilde{; ; ; sl_2}; ; ; =\widehat{; ; ; sl_2}; ; ; + C d $ with the same Whittaker function and central charge. We have to modulo a central character for $sl_2$ to obtain simple degenerate Whittaker $\widehat{; ; ; sl_2}; ; ; $-modules with noncritical level. In the case of critical level the universal Whittaker module is reducible. We prove that the quotient of universal Whittaker $\widehat{; ; ; sl_2}; ; ; $--module by a submodule generated by a scalar action of central elements of the vertex algebra $V_{; ; ; -2}; ; ; (sl_2)$ is simple as $\widehat{; ; ; \sl_2}; ; ; $--module. We also explicitly describe the simple quotients of universal Whittaker modules at the critical level for $\widetilde{; ; ; \sl_2}; ; ; $. Quite surprisingly, with the same Whittaker function some simple degenerate $\widetilde{; ; ; sl_2}; ; ; $ Whittaker modules at the critical level have semisimple action of $d$ and others have free action of $d$. At last, by using vertex algebraic techniques we present a Wakimoto type construction of a family of simple generalized Whittaker modules for $\widehat{; ; ; sl_2}; ; ; $ at the critical level. This family includes all classical Whittaker modules at critical level. We also have Wakimoto type realization for degenerate Whittaker modules for $\widehat{; ; ; sl_2}; ; ; $ at noncritical level.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


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

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Dražen Adamović, (196061)

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka:


  • MathSciNet
  • Zentralblatt für Mathematik


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