Related papers: A character relationship between symmetric group a…
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…
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…
A general setting to study a certain type of formulas, expressing characters of the symmetric group $\mathfrak{S}_n$ explicitly in terms of descent sets of combinatorial objects, has been developed by two of the authors. This theory is…
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,…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
Block character of a finite symmetric group S(n) is a positive definite function which depends only on the number of cycles in permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the…
We determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups S_n and their double covers. In particular, we give a simple computation,…
We construct a subalgebra of dimension $2.3^{n-1}$ of the group algebra of a Weyl group of type $B_n$ containing its Solomon descent's algebra but also the Solomon's descent algebra of the symmetric group. This lead us to a construction of…
Applying the embedding of $A_{n-1}$ in $B_n$, $C_n$ and $D_n$ we construct a new supercharacter theory for the Sylow subgroups in orthogonal and symplectic groups over a finite field. The constructed supercharacter appears to be a little…
We use binary trees to study the Bratteli diagram of Sylow 2-subgroups of symmetric groups. We show that it is simple, has a recursive structure, and self-similarities at all scales. We contrast its subgraph of one-dimensional…
We show how decreasing diagrams introduced in the theory of rewriting systems can be used to prove coherence type theorems in category theory. We apply this method to describe a coherent presentation of the $0$-Hecke monoid…
In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.
In this work we uncover a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes…
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a…
We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding Poisson algebra of classical polynomial symbols. Several…
In this paper, we derive a relation of new kind between certain character values of symmetric groups in terms of so-called maya diagrams. We also investigate a relation between our result and Bernstein's creation operators for Schur…
We prove that $(\mathbb{Z}_k \wr \mathcal{S}_n \times \mathbb{Z}_k \wr \mathcal{S}_{n-1}, \text{diag} (\mathbb{Z}_k \wr \mathcal{S}_{n-1}) )$ is a symmetric Gelfand pair, where $\mathbb{Z}_k \wr \mathcal{S}_n$ is the wreath product of the…
We state combinatorial formulas for hyperoctahedral group ($\mathfrak B_n$) character evaluations of the form $\chi( {{\widetilde C}_w}^{\negthickspace\negthickspace BC}\negthickspace(1))$, where ${{\widetilde…
By exploiting relationships between the values taken by ordinary characters of symmetric groups we prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd…