Quasi-lisse extension of affine sl2 à la Feigin–Tipunin - Creutzig, Thomas; Nakatsuka, Shigenori; Sugimoto, Shoma (Advances in Mathematics, 2024)
We study the affine analogue FTp(sl2) of the triplet algebra. We show that FTp(sl2) is quasi-lisse and the associated variety is the nilpotent cone of sl2. We realize FTp(sl2) as the global sections of a sheaf of vertex algebras in the spirit of Feigin–Tipunin and thereby construct infinitely many simple modules and, in particular solve a conjecture by Semikhatov and Tipunin. We introduce the Kazama–Suzuki dual superalgebra sWp(sl2|1) of FTp(sl2) and their singlet type subalgebras sMp(sl2|1) and Mp(sl2) and show their correspondence of categories. For p=1, we show the logarithmic Kazhdan–Lusztig correspondence for these (super)algebras and, in particular, show that the quantum group corresponding to sMp(sl2|1) is the unrolled restricted quantum supergroup u−1H(sl2|1) as suggested by Semikhatov and Tipunin.
CRIS-Team Scopus Importer:2024-06-24
Keywords: Affine vertex algebras; Feigin-Tipunin type extensions; Logarithmic Kazhdan-Lusztig correspondence; Nilpotent cone