Related papers: Reducing mod p complex representations of finite r…
We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.
We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.
We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.
I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.
We propose upper bounds for the number of modular constituents of the restriction modulo $p$ of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.
In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.
We classify all finite groups that have lifting property of mod $p$ representations to mod $p^2$ representations for all prime $p$.
We determine the finite groups whose real irreducible representations have different degrees.
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…
For the group of endo-permutation modules of a finite \(p\)-group, there is a surjective reduction modulo \(p\) homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic \(p\). We prove…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin's weight conjecture on the $p$-blocks of a finite group would imply some arithmetical conditions on the…
In this paper, we prove the FPP conjecture, giving a strong upper bound on the unitary dual of a real reductive group. Our proof is an application of the global generation properties of $\mathcal{D}$-modules on the flag variety and their…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…
We introduce a spreading out technique to deduce finiteness results for \'etale fundamental groups of complex varieties by characteristic $p$ methods, and apply this to recover a finiteness result proven recently for local fundamental…