21 citations · 38 across the 17 of their papers we have counts for
27 papers
Simple Harish-Chandra bimodules in positive characteristics
Lewis Groves, Lewis Topley, Matthew Westaway
Let be a standard reductive group over an algebraically closed field of positive characteristic and let . The category of Harish-Chandra b…
Parabolic induction for modular finite -algebras
Simon Goodwin, Lewis Topley, Matt Westaway
We study the modules of minimal dimension for reduced enveloping algebras of Lie algebras of reductive algebraic groups using the theory of modular finite -algebras. First of al…
Modular representations of the Yangian
Hao Chang, Jinxin Hu, Lewis Topley
Let be the Yangian associated to the general linear Lie algebra , defined over an algebraically closed field $\mathbbm{k}$ of characteristic . In this…
Equivariant deformation theory for nilpotent slices in symplectic Lie algebras
Filippo Ambrosio, Lewis Topley
The Slodowy slice is a flat Poisson deformation of its nilpotent part, and it was demonstrated by Lehn-Namikawa-Sorger that there is an interesting infinite family of nilpotent orb…
On induced completely prime primitive ideals in enveloping algebras of classical Lie algebras
Simon M. Goodwin, Lewis Topley, Matthew Westaway
A distinguished family of completely prime primitive ideals in the universal enveloping algebra of a reductive Lie algebra over are those ideals const…
Modular Representations of Truncated current Lie algebras
Matthew Chaffe, Lewis Topley
In this paper we consider the structure and representation theory of truncated current algebras associated to the Lie algebra $\mathfra…
The centre of the modular affine vertex algebra
Tomoyuki Arakawa, Lewis Topley, Juan J. Villarreal
The Feigin--Frenkel theorem states that, over the complex numbers, the centre of the universal affine vertex algebra at the critical level is an infinite rank polynomial algebra. T…
Category for truncated current Lie algebras
Matthew Chaffe, Lewis Topley
In this paper we study an analogue of the Bernstein--Gelfand--Gelfand category for truncated current Lie algebras attached to a complex semisimple Li…
Parabolic induction for Springer fibres
Lewis Topley, Neil Saunders
Let be a reductive group satisfying the standard hypotheses, with Lie algebra . For each nilpotent orbit in a Levi subalgebra we…
One dimensional representations of finite -algebras, Dirac reduction and the orbit method
Lewis Topley
In this paper we study the variety of one dimensional representations of a finite -algebra attached to a classical Lie algebra, giving a precise description of the dimensions of…
Modular representations of Lie algebras of reductive groups and Humphreys' conjecture
Alexander Premet, Lewis Topley
Let be connected reductive algebraic group defined over an algebraically closed field of characteristic and suppose that is a good prime for the root system of ,…
Universal filtered quantizations of nilpotent Slodowy slices
Filippo Ambrosio, Giovanna Carnovale, Francesco Esposito +1
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by sh…
Restricted shifted Yangians and restricted finite -algebras
Simon M. Goodwin, Lewis Topley
We study the truncated shifted Yangian over an algebraically closed field of characteristic , which is known to be isomorphic to the finite -alg…
A proof of the first Kac-Weisfeiler conjecture in large characteristics
Benjamin Martin, David Stewart, Akaki Tikaradze +1
In 1971, Kac and Weisfeiler made two influential conjectures describing the dimensions of simple modules of a restricted Lie algebra . The first predicts the maximal…
Smoothness of stabilisers in generic characteristic
Benjamin Martin, David I. Stewart, Lewis Topley
Let be a commutative unital ring. Given a finitely presented affine -group scheme acting on a separated scheme of finite type over , we show that there is a prime…
Minimal dimensional representations of reduced enveloping algebras for
Simon M. Goodwin, Lewis Topley
Let , where is an algebraically closed field of characteristic , and . Let and denote by…
The Orbit Method for Poisson Orders
Stephane Launois, Lewis Topley
A version of Kirillov's orbit method states that the primitive spectrum of a generic quantisation of a Poisson algebra should correspond bijectively to the symplectic leave…
The p-centre of Yangians and shifted Yangians
Jonathan Brundan, Lewis Topley
We study the Yangian associated to the general linear Lie algebra over a field of positive characteristic, as well as its shifted analog . Our main…
On the semi-centre of a Poisson algebra
Cesar Lecoutre, Lewis Topley
If is a Lie algebra then the semi-centre of the Poisson algebra is the subalgebra generated by ad-eigenvectors. In this paper we ab…
Transfer results for Frobenius extensions
Stephane Launois, Lewis Topley
We study Frobenius extensions which are free-filtered by a totally ordered, finitely generated abelian group, and their free-graded counterparts. First we show that the Frobenius p…
Modular finite -algebras
Simon M. Goodwin, Lewis W. Topley
Let be an algebraically closed field of characteristic and let be a connected reductive algebraic group over . Under some standard hypothesis on , we give a d…
A non-restricted counterexample to the first Kac-Weisfeiler conjecture
Lewis Topley
In 1971 Kac and Weisfeiler made two important conjectures regarding the representation theory of restricted Lie algebras over fields of positive characteristic. The first of these…
Harish-Chandra invariants and the centre of the reduced enveloping algebra
Lewis W. Topley
In this article we consider the centre of the reduced enveloping algebra of the Lie algebra of a reductive algebraic group in very good characteristic p > 2. The Harish-Chandra cen…
A Morita theorem for modular finite W-algebras
Lewis Topley
We consider the Lie algebra of a simple, simply connected algebraic group over a field of large positive characteristic. For each nilpotent orbit $\mathcal{O} \subse…