Quasi-lisse extension of affine sl2 à la Feigin–Tipunin

Creutzig T, Nakatsuka S, Sugimoto S (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Advances in Mathematics Elsevier

Book Volume: 448

Article Number: 109717

DOI: 10.1016/j.aim.2024.109717

Abstract

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.

Involved external institutions

University of Alberta CA Canada (CA) Kyushu University / 九州大学 JP Japan (JP)

How to cite

APA:

Creutzig, T., Nakatsuka, S., & Sugimoto, S. (2024). Quasi-lisse extension of affine sl2 à la Feigin–Tipunin. Advances in Mathematics, 448. https://doi.org/10.1016/j.aim.2024.109717

MLA:

Creutzig, Thomas, Shigenori Nakatsuka, and Shoma Sugimoto. "Quasi-lisse extension of affine sl2 à la Feigin–Tipunin." Advances in Mathematics 448 (2024).

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