Related papers: Restriction of characters to subgroups of wreath p…

Let $G$ be a finite group with $k$ conjugacy classes, and $S(\infty)$ be the infinite symmetric group, i.e. the group of finite permutations of $\left\{1,2,3,\ldots\right\}$. Then the wreath product $G_{\infty}=G\sim S(\infty)$ of $G$ with…

For a finite group, it is interesting to determine when two ordinary irreducible representations have the same $p$-modular reduction; that is, when two rows of the decomposition matrix in characteristic $p$ are equal, or equivalently when…

Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such…

For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our…

In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable…

We study irreducible restrictions from modules over symmetric groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. Such results are known when the…

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…

We give closed product formulas for the irreducible characters of the symmetric groups related to rectangular `almost square' Young diagrams $p \times(p+\delta)$ for a fixed value of an integer $\delta$ and an arbitrary integer $p$.

The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the Ariki-Koike version of the Murnaghan-Nakayama rule by vertex algebraic methods, we…

The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…

Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the sequence of p-adic groups $\{GL_n(F)\}_{n=0}^\infty$, with multiplication defined through parabolic induction. We study the problem of the…

This note presents a procedure to determine the reduction of the irreducible and the induced characters of the symmetric group in terms of the irreducible and induced characters of the hyperoctahedral group Key Words: Symmetric Group,…

Let G be a p-solvable group, P a p-subgroup and chi in Irr(G) such that chi(1)_p \ge |G:P|_p. We prove that the restriction chi_P is a sum of characters induced from subgroups Q\le P such that chi(1)_p=|G:Q|_p. This generalizes previous…

For a prime $p$, we determine a Sylow $p$-subgroup $D$ of a finite group $G$ such that the principal $p$-block $B$ of $G$ has four irreducible ordinary characters. It has been determined already for the cases where the number is up to three…

Using the theory of Macdonald, Gordon showed that the graded characters of the simple modules for the restricted rational Cherednik algebra by Etingof and Ginzburg associated to the symmetric group $\mathfrak{S}_n$ are given by…

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be…

Let $G$ be a finite solvable or symmetric group and let $B$ be a $2$-block of $G$. We construct a canonical correspondence between the irreducible characters of height zero in $B$ and those in its Brauer first main correspondent. For…

The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…

A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…

We parametrize the set of irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\mathrm{D}_6(q)$ and $\mathrm{E}_6(q)$, for an arbitrary power $q$ of any prime $p$. In particular, we establish that the parametrization…