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Felix Noeske

Publications and source records attributed to Felix Noeske.

8 recordsLinked to original sources
arXiv2013

Broué's abelian defect group conjecture and 3-decomposition numbers of the sporadic simple Conway group Co_1

In the representation theory of finite groups, Broué's abelian defect group conjecture says that for any prime p if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the normaliser N_G(P) of P in G are derived equivalent. We prove that Broué's conjecture, and even Rickard's splendid equivalence conjecture, are true for the unique 3-block A of defect 2 of the sporadic simple Conway group Co_1, implying that both conjectures hold for all 3-blocks of Co_1. To do so, we determine the 3-decomposition numbers of A, and we actually show that A is Puig equivalent to the principal 3-block of the symmetric group S_6 of degree 6.

math.RT↗
arXiv2013

Restricting unipotent characters in special orthogonal groups

For all prime powers q we restrict the unipotent characters of the special orthogonal groups SO_5(q) and SO_7(q) to a maximal parabolic subgroup. We determine all irreducible constituents of these restrictions for SO_5(q) and a large part of the irreducible constituents for SO_7(q).

math.RT↗
arXiv2013

Decomposition numbers of SO_7(q) and Sp_6(q)

We complete the l-modular decomposition numbers of the unipotent characters in the principal block of the special orthogonal groups SO_7(q) and the symplectic groups Sp_6(q) for all prime powers q and all odd primes l different from the defining characteristic.

math.RT↗
arXiv2012

Broué's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group

In the representation theory of finite groups, there is a well-known and important conjecture, due to Broué saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the normaliser N_G(P) of P in G are derived equivalent. We prove in this paper, that Broué's abelian defect group conjecture, and even Rickard's splendid equivalence conjecture are true for the faithful 3-block A with an elementary abelian defect group P of order 9 of the double cover 2.HS of the Higman-Sims sporadic simple group. It then turns out that both conjectures hold for all primes p and for all p-blocks of 2.HS.

math.RT↗
arXiv2011

Broué's abelian defect group conjecture holds for the sporadic simple Conway group Co_3

In the representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block A_N of the normaliser N_G(P) of P in G are derived equivalent (Rickard equivalent). This conjecture is called Strong Version of Broué's Abelian Defect Group Conjecture. In this paper, we prove that the strong version of Broué's abelian defect group conjecture is true for the non-principal 2-block A with an elementary abelian defect group P of order 8 of the sporadic simple Conway group Co_3. This result completes the verification of the strong version of Broué's abelian defect group conjecture for all primes p and for all p-blocks of Co_3.

math.RT↗
arXiv2008

The Imprimitive Faithful Complex Characters of the Schur Covers of the Symmetric and Alternating Groups

Using combinatorics and character theory, we determine the imprimitive faithful complex characters, i.e., the irreducible faithful complex characters which are induced from proper subgroups, of the Schur covers of the symmetric and alternating groups. Furthermore, for every imprimitive character we establish all its minimal block stabilizers. As a corollary, we also determine the monomial faithful characters of the Schur covers.

math.GR↗