12 papers
The Kazhdan-Lusztig category of W-algebras of simply-laced Lie algebras at irrational levels
Thomas Creutzig, Gurbir Dhillon, Shigenori Nakatsuka
Let be a simple, simply-laced Lie algebra and nilpotent. The Kazhdan-Lusztig category of the W-algebra associated with $(\…
Center of the affine at the critical level and pseudo-differential operators
Dražen Adamović, Boris Feigin, Shigenori Nakatsuka
We prove that the center of the affine Lie algebra at the critical level is generated by the coefficients in the expansion of the pseudo-differentia…
Quantum Hamiltonian reductions for W-algebras
Justine Fasquel, Shigenori Nakatsuka
In this paper, we establish a general criterion for good pairs, namely pairs consisting of a nilpotent orbit and an even good grading in a simple Lie algebra, which guarantees the…
Minimal W-algebras of at level minus one
Thomas Creutzig, Justine Fasquel, Vladimir Kovalchuk +2
For we show that the simple minimal -algebra of at level minus one is isomorphic to the even subalgebra of the tensor produ…
Center of affine at the critical level
Drazen Adamovic, Shigenori Nakatsuka
In this article, we shall describe the center of the universal affine vertex superalgebra associated with $\mathfrak g=\mathfrak{sl}_{2|1}, \mathfrak {gl}_{2…
On Virasoro-type reductions and inverse Hamiltonian reductions for -algebras and -algebras
Justine Fasquel, Vladimir Kovalchuk, Shigenori Nakatsuka
In this article, the Virasoro-type reduction and the corresponding inverse reductions are established for W-algebras associated with classical Lie type and nilpotent orbits of heig…