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The projective cover of the trivial module in characteristic for the sporadic simple Janko group revisited
Jürgen Müller
This is a sequel to arXiv:2509.05805 [math.RT], where we have determined the -modular projective indecomposable summands of the permutation character of on the cosets of…
Is the projective cover of the trivial module in characteristic for the sporadic simple Janko group a permutation module?
Jürgen Müller
We determine the ordinary character of the projective cover of the trivial module in characteristic for the sporadic simple Janko group , and answer the question posed in…
On low-degree representations of the symmetric group
Jürgen Müller
The aim of the present paper is to obtain a classification of all the irreducible modular representations of the symmetric group on letters of dimension at most , includin…
Broué's abelian defect group conjecture for the sporadic simple Janko group J_4 revisited
Shigeo Koshitani, Jürgen Müller, Felix Noeske
We show that the 3-block of the sporadic simple Janko group J_4 with defect group C_3 x C_3, and the principal 3-block of the alternating group A_8 are Puig equivalent, answering a…
Broué's abelian defect group conjecture holds for the Harada-Norton sporadic simple group
Shigeo Koshitani, Jürgen Müller
In representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime , if a -block of a finite gr…