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Register a new userSheets and associated varieties of affine vertex algebras
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We show that sheet closures appear as associated varieties of affine vertex algebras. Further, we give new examples of non-admissible affine vertex algebras whose associated variety is contained in the nilpotent cone. We also prove some conjectures from our previous paper and give new examples of lisse affine W-algebras.
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We investigate the irreducibility of the nilpotent Slodowy slices that appear as the associated variety of W-algebras. Furthermore, we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves.
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference Hamiltonian equations. We establish relations of these notions to $q$-deformed $W$-algebras and lattice Poisson algebras. We introduce the notion of Adler type pseudodifference operators and apply them to integrability of differential-difference Hamiltonian equations.
Let G be a split semi-simple p-adic group and let H be its Iwahori-Hecke algebra with coefficients in the algebraic closure k of the finite field with p elements. Let F be the affine flag variety over k associated with G. We show, in the simply connected simple case, that a torus-equivariant K-theory of F (with coefficients in k) admits an H-action by Demazure operators and that this provides a model for the regular representation of H.
We introduce a new family of affine $W$-algebras associated with the centralizers of arbitrary nilpotent elements in $mathfrak{gl}_N$. We define them by using a version of the BRST complex of the quantum Drinfeld--Sokolov reduction. A family of free generators of the new algebras is produced in an explicit form. We also give an analogue of the Fateev--Lukyanov realization for these algebras by applying a Miura-type map.
In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related to the $p$-centers of the Virasoro algebra and affine Lie algebras. Among the main results, we classify their irreducible $mathbb{N}$-graded modules by explicitly determining their Zhu algebras and show that these vertex algebras have only finitely many irreducible $mathbb{N}$-graded modules and they are $C_2$-cofinite.
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