相关论文: Irreducible Symmetric Group Characters of Rectangu…

Proving a conjecture of Miller, we show that as $n$ tends to infinity almost all entries in the character table of $S_n$ are divisible by any given prime power. This extends our earlier work which treated divisibility by primes.

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…

We consider problems concerning the largest degrees of irreducible characters of symmetric groups, and the multiplicities of character degrees of symmetric groups. Using evidence from computer experiments, we posit several new conjectures…

We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

Let $S_n$ denote a symmetric group, $\chi$ an irreducible character of $S_n$, and $g\in S_n$ an element which decomposes into $k$ disjoint cycles, where $1$-cycles are included. Then $|\chi(g)|\le k!$, and this upper bound is sharp for…

The covering number of a non-linear character $\chi$ of a finite group $G$ is the least positive integer $k$ such that every irreducible character of $G$ occurs in $\chi^k$. We determine the covering numbers of irreducible characters of the…

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…

Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of…

Amdeberhan recently proposed certain equalities between sums in the character table of symmetric groups. These equalities are between signed column sums in the character table, summing over the rows labeled by partitions in $\Ev$, where…

In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.

For any positive integer $N$, we describe a natural complex representation of the symmetric group $\Sigma_N$ on the vector space spanned by its involutions that contains each irreducible representation exactly once.

We study the zero-sharing behavior among irreducible characters of a finite group. For symmetric groups $S_n$, it is proved that, with one exception, any two irreducible characters have at least one common zero. To further explore this…

Suppose that $\chi_\lambda$ and $\chi_\mu$ are distinct irreducible characters of the symmetric group $S_n$. We give an algorithm that, in time polynomial in $n$, constructs $\pi\in S_n$ such that $\chi_\lambda(\pi)$ is provably different…

The aim of the present paper is to obtain a classification of all the irreducible modular representations of the symmetric group on $n$ letters of dimension at most $n^3$, including dimension formulae. This is achieved by improving an idea,…

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…

Formulas for the expansion of arbitrary invariant group functions in terms of the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a combinatorial method. The method is similar to one used by Balantekin to expand…

We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on square matrices, which we refer to as the recombinant, agrees…

We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.