Related papers: Irreducible projective characters of wreath produc…
The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.
In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor…
In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.
We give a new formula for the values of an irreducible character of the symmetric group S_n indexed by a partition of rectangular shape. Some observations and a conjecture are given concerning a generalization to arbitrary shapes.
A character identity which relates irreducible character values of the hyperoctahedral group $B_n$ to those of the symmetric group $S_{2n}$ was recently proved by L\"ubeck and Prasad. Their proof is algebraic and involves Lie theory. We…
The Alperin--McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its $p$-local subgroups. A refinement of this conjecture was stated by the author in a previous paper. We prove that this…
A relation between certain irreducible character values of the hyperoctahedral group $B_n$ ($\mathbb{Z}/2\mathbb{Z} \wr S_n$) and the symmetric group $S_{2n}$ was proved by F. L\"ubeck and D. Prasad in 2021. Their proof is algebraic in…
In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify…
We characterise the group property of being with infinite conjugacy classes for wreath products of groups
In 1911 Schur computed the spin character values of the symmetric group using two important ingredients: the first one later became famously known as the Schur Q-functions and the second one was certain creative construction of the…
In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.
We consider non-trivial irreducible tensor products of modular representations of a symmetric group $S_n$ in characteristic 2 for even $n$ completing the proof of a classification conjecture of Gow and Kleshchev about such products.
In this paper, we give the decomposition into irreducible characters of the restriction to the wreath product $\mathbb{Z}_{p-1} \wr \mathfrak{S}_w$ of any irreducible character of $(\mathbb{Z}_p \rtimes \mathbb{Z}_{p-1}) \wr…
The irreducible characters of the symmetric group are a symmetric polynomial in the eigenvalues of a permutation matrix. They can therefore be realized as a symmetric function that can be evaluated at a set of variables and form a basis of…
Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…
We show that the wreath product of two finite symmetric or alternating groups is 2-generated.
We give a new formula for the irreducible spin characters of the symmetric groups. This formula is analogous to Stanley's character formula for the usual (linear) characters of the symmetric groups.
For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$, or more generally, which representations remain homogeneous in characteristic $p$. In this paper we…
Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…
In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…