The Number of Conjugacy Classes in a Finite Group.
The number of indecomposable Schur rings over a cyclic 2-group.
The number of representations of a group induced from the irreducible representations of a normal subgroup.
The Ore conjecture
The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.
The other -theorem
The parametrization of interior algebras.
The periodicity conjecture for blocks of group algebras
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
The primitive distance-transitive representations of the Fischer groups.
The Primitive Permutation Groups of Some Special Degrees.
The rank of G0 for polycyclic group algebras
The ranks of primitive parabolic permutation representations of the simple groups , , and .
The relationship between Zhedanov's algebra and the double affine Hecke algebra in the rank one case.
The representation theory and the branching graph for the family of Turaev algebras .
The representations and generic degrees of the Hecke algeba of type H4.
The ring of multisymmetric functions
We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
The Roquette category of finite -groups
Let be a prime number. This paper introduces the Roquette category of finite -groups, which is an additive tensor category containing all finite -groups among its objects. In , every finite -group admits a canonical direct summand , called the edge of . Moreover splits uniquely as a direct sum of edges of Roquette -groups, and the tensor structure of can be described in terms of such edges. The main motivation for considering this category is that the additive functors from to...
The Schur Multiplicator of SL(2, Z/mZ) and the Congruence Subgroup Property.
The Schur Multipliers of Sp6(Z),Spin8(Z),Spin7(Z),andF4(Z).
The special circulant matrix and units in group rings.
The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group
We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair .