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Jyotirmoy Ganguly

Publications and source records attributed to Jyotirmoy Ganguly.

8 recordsLinked to original sources
arXiv2026

Stiefel-Whitney classes for symmetric groups

We prove several results about Stiefel-Whitney Classes (SWCs) $w_k(π)$ of representations $π$ of $S_n$. First, each SWC is polynomial in the character values of $π$ at involutions. Next, for a fixed $k$, the proportion of irreducible $π$ for which $w_k(π)=0$ approaches $100\%$ as $n \to \infty$. A similar result holds for the top SWCs. We also provide a simple criterion which determines the first nonvanishing SWC for a representation. The first four SWCs are computed explicitly. Finally, we give analogues for alternating groups.

math.RT↗
arXiv2025

Kronecker Coefficients and Simultaneous Conjugacy Classes

A Kronecker coefficient is the multiplicity of an irreducible representation of a finite group $G$ in a tensor product of irreducible representations. We define Kronecker Hecke algebras and use them as a tool to study Kronecker coefficients in finite groups. We show that the number of simultaneous conjugacy classes in a finite group $G$ is equal to the sum of squares of Kronecker coefficients, and the number of simultaneous conjugacy classes that are closed under elementwise inversion is the sum of Kronecker coefficients weighted by Frobenius-Schur indicators. We use these tools to investigate which finite groups have multiplicity-free tensor products. We introduce the class of doubly real groups, and show that they are precisely the real groups which have multiplicity-free tensor products. We show that non-Abelian groups of odd order, non-Abelian finite simple groups, and most finite general linear groups do not have multiplicity-free tensor products.

math.RT↗
arXiv2025

Divisibility of Character Values of Representations of Coxeter Groups

Let $d$ be a positive integer. We study the proportion of irreducible characters of infinite families of irreducible Coxeter groups whose values evaluated on a fixed element $g$ are divisible by $d$. For Coxeter groups of types $A_n, B_n$ and $D_n$, the proportion tends to $1$ as $n$ approaches infinity. For Dihedral groups, which are Coxeter groups of type $I_2(n)$, we compute the limit of the proportion.

math.RT↗
arXiv2021

Stiefel Whitney Classes for Real representations of $\mathrm{GL}_2(\mathbb{F}_q)$

We compute the total Stiefel Whitney class for a real representation $π$ of $\mathrm{GL}_2(\mathbb{F}_q)$, where $q$ is odd. The obstruction class of $π$ is defined to be the Stiefel Whitney class of lowest positive degree that does not vanish. We provide an expression for the obstruction class of $π$ in terms of its character values if $\detπ=1$.

math.RT↗
arXiv2020

Spinorial Representations of Orthogonal Groups

Let $G$ be a real compact Lie group, such that $G=G^0\rtimes C_2$, with $G^0$ simple. Here $G^0$ is the connected component of $G$ containing the identity and $C_2$ is the cyclic group of order $2$. We give a criterion for whether an orthogonal representation $π: G \to \mathrm{O}(V)$ lifts to $\mathrm{Pin}(V)$ in terms of the highest weights of $π$. We also calculate the first and second Stiefel-Whitney classes of the representations of the Orthogonal groups.

math.RT↗
arXiv2019

Spinorial Representations of Symmetric Groups

A real representation $π$ of a finite group may be regarded as a homomorphism to an orthogonal group $\Or(V)$. For symmetric groups $S_n$, alternating groups $A_n$, and products $S_n \times S_{n'}$ of symmetric groups, we give criteria for whether $π$ lifts to the double cover $\Pin(V)$ of $\Or(V)$, in terms of character values. From these criteria, we compute the second Stiefel-Whitney classes of these representations.

math.RT↗
arXiv2019

On the Divisibility of Character Values of the Symmetric Group

Fix a partition $μ=(μ_1,\dotsc,μ_m)$ of an integer $k$ and positive integer $d$. For each $n>k$, let $χ^λ_μ$ denote the value of the irreducible character of $S_n$ at a permutation with cycle type $(μ_1,\dotsc,μ_m,1^{n-k})$. We show that the proportion of partitions $λ$ of $n$ such that $χ^λ_μ$ is divisible by $d$ approaches $1$ as $n$ approaches infinity.

math.RT↗