6 citations · 12 across the 10 of their papers we have counts for
18 papers · 1 filter
RoCK blocks for double covers of symmetric groups over a complete discrete valuation ring
Alexander Kleshchev, Michael Livesey
Recently the authors proved the existence of RoCK blocks for double covers of symmetric groups over an algebraically closed field of odd characteristic. In this paper we prove that…
RoCK blocks for double covers of symmetric groups and quiver Hecke superalgebras
Alexander Kleshchev, Michael Livesey
We define and study RoCK blocks for double covers of symmetric groups. We prove that RoCK blocks of double covers are Morita equivalent to standard `local' blocks. The analogous re…
Picard groups for blocks with normal defect groups and linear source bimodules
Michael Livesey, Claudio Marchi
It is an open problem as to whether any bimodule inducing a Morita auto-equivalence of a block must have endopermutation source. We prove that, for blocks with normal defect gr…
Arbitrarily large Morita Frobenius numbers
Florian Eisele, Michael Livesey
We construct blocks of finite groups with arbitrarily large Morita Frobenius numbers, an invariant which determines the size of the minimal field of definition of the associated ba…
Donovan's conjecture and extensions by the centralizer of a defect group
Charles W. Eaton, Michael Livesey
We consider Donovan's conjecture in the context of blocks of groups with defect group and normal subgroups such that , extending similar results…
Linear source invertible bimodules and Green correspondence
Markus Linckelmann, Michael Livesey
We show that the Green correspondence induces an injective group homomorphism from the linear source Picard group of a block of a finite group algebra to the l…
On Picent for blocks with normal defect group
Michael Livesey, Claudio Marchi
We prove that if is a block of a finite group with normal abelian defect group and inertial quotient a direct product of elementary abelian groups, then $\operatorname{Picent}(…
Arbitrarily large -Morita Frobenius numbers
Michael Livesey
We construct blocks of finite groups with arbitrarily large -Morita Frobenius numbers. There are no known examples of two blocks defined over that are no…
On Picard groups of blocks with normal defect groups
Michael Livesey
Let be a block with normal abelian defect group and abelian inertial quotient. We prove that every Morita auto-equivalence of has linear source. We note that this improves…
Some examples of Picard groups of blocks
Charles W. Eaton, Michael Livesey
We calculate examples of Picard groups for 2-blocks with abelian defect groups with respect to a complete discrete valuation ring. These include all blocks with abelian 2-groups of…
Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings
Charles W. Eaton, Florian Eisele, Michael Livesey
We give a reduction to quasisimple groups for Donovan's conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring . C…
Donovan's conjecture and blocks with abelian defect groups
Charles Eaton, Michael Livesey
We give a reduction of Donovan's conjecture for abelian groups to a similar statement for quasisimple groups. Consequently we show that Donovan's conjecture holds for abelian -g…
Towards Donovan's conjecture for abelian defect groups
Charles Eaton, Michael Livesey
We define a new invariant for a -block, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an a…
Classifying blocks with abelian defect groups of rank for the prime
Charles Eaton, Michael Livesey
In this paper we classify all blocks with defect group up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes th…
Loewy lengths of blocks with abelian defect groups
Charles W. Eaton, Michael Livesey
We consider -blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index . Using th…
A note on perfect isometries between finite general linear and unitary groups at unitary primes
Michael Livesey
Let be a power of a prime, a prime not dividing , a positive integer coprime to both and the multiplicative order of and a positive integer. A. Wat…
Broué's perfect isometry conjecture holds for the double covers of the symmetric and alternating groups
Michael Livesey
O. Brunat and J. Gramain recently proved that any two blocks of double covers of symmetric groups are Broué perfectly isometric provided they have the same weight and sign. They al…
On Rouquier Blocks for Finite Classical Groups at Linear Primes
Michael Livesey
H. Miyachi and W. Turner have independently proved that Broue's Abelian Defect Group Conjecture holds for certain unipotent blocks of the finite general linear group, the so-called…