arXiv subjects

Amrutha P

Publications and source records attributed to Amrutha P.

3 recordsLinked to original sources

arXiv2024

Cyclic Characters of Alternating Groups

We determine the eigenvalues with multiplicity of each element of an alternating group in any irreducible representation. This is equivalent to determining the decomposition of cyclic representations of alternating groups into irreducibles. We characterize pairs $(w, V)$, where $w$ is an element and $V$ is an irreducible representation of an alternating group such that $w$ admits a non-zero invariant vector in $V$. We also establish large new families of global conjugacy classes for alternating groups, thereby giving a new proof of a result of Heide and Zalessky on the existence of such classes.

math.RT↗

arXiv2023

On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups

We determine when a permutation with cycle type $\mu$ admits a non-zero invariant vector in the irreducible representation $V_\lambda$ of the symmetric group. We find that a majority of pairs $(\lambda,\mu)$ have this property, with only a few simple exceptions.

math.RT↗

arXiv2020

On the determinant of representations of generalized symmetric groups

In this paper we study the determinant of irreducible representations of the generalized symmetric groups $\mathbb{Z}_r \wr S_n$. We give an explicit formula to compute the determinant of an irreducible representation of $\mathbb{Z}_r \wr S_n$. Recently, several authors have characterized and counted the number of irreducible representations of a given finite group with nontrivial determinant. Motivated by these results, for given integer $n$, $r$ an odd prime and $ζ$ a nontrivial multiplicative character of $\mathbb{Z}_r \wr S_n$ with $n<r$, we obtain an explicit formula to compute $N_ζ(n)$, the number of irreducible representations of $\mathbb{Z}_r \wr S_n$ whose determinant is $ζ$.

math.RT↗