Krishnendu Gongopadhyay

activity

20052026

most citedPalindromic Automorphisms of Free Groups

10 citations · 55 across the 60 of their papers we have counts for

collaborators

Showing math.GRShow all

35 papers · 1 filter

math.GR2026

Reversibility and its asymptotic counting in Picard group

Debattam Das, Krishnendu Gongopadhyay, Anirban Mukhopadhyay

We investigate reversible elements in the Picard modular group $PSL (2, Z [i])$ . We show that reversibility coincides with strong reversibility for Kleinian groups,…

math.GR2026

On the Product of Coninvolutory Affine Transformations

Sandipan Dutta, Krishnendu Gongopadhyay, Rahul Mondal

A complex matrix is called \emph{coninvolutory} if $T T = I$ . In this paper, we study decompositions of affine transformations in $\mathrm{Aff}(n,\mathbb{C})=\mathrm{GL}(n,…

math.GR2025

Classification of Quaternionic Projective Transformations by Equicontinuity Regions

Sandipan Dutta, Krishnendu Gongopadhyay, Rahul Mondal

We describe the equicontinuity regions of cyclic subgroups of the quaternionic projective linear group $PSL (n + 1, H)$ . We show that these regions depend solely on t…

math.GR2025

Strongly Doubly Reversible Pairs in Quaternionic Unitary Group of Signature $(n, 1)$

Krishnendu Gongopadhyay, Sagar B. Kalane

Let $PSp (n, 1)$ denote the isometry group of quaternionic hyperbolic $n$ --space $\h^n$. A pair $(g_{1}, g_{2}) \in PSp (n, 1)^{2}$ is \emph{strongly doubly reversible} if $(g…

math.GR2025

Conjugate reversibility in complex special linear groups

Krishnendu Gongopadhyay, Rahul Mondal

We introduce and study conjugate reversibility (or $c$ -reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex co…

math.GR2025

Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

We estimate the asymptotic growth of reciprocal conjugacy classes in Hecke groups using their free product structure and word lengths of reciprocal elements. Our approach is differ…

math.GR2025

Kulkarni limit sets for cyclic quaternionic projective groups

Sandipan Dutta, Krishnendu Gongopadhyay, Rahul Mondal

We consider the natural action of the quaternionic projective linear group $PSL (n + 1, H)$ on the quaternionic projective space $P_{H}^{n}$ . We compu…

math.GR2024

On the almost palindromic width of certain free constructions of groups

Krishnendu Gongopadhyay, Shrinit Singh

We provide a general structural criterion implying that a group has infinite $m$ -almost palindromic width. In particular, we prove that both HNN extensions and free products exhibi…

math.GR2024

On the $z$ -classes of Palindromic automorphisms of Free Groups

Krishnendu Gongopadhyay, Lokenath Kundu, Shashank Vikram Singh

The palindromic automorphism group is a subgroup of the automorphism group $A u t (F_{3}) .$ We establish a necessary and sufficient condition for a matrix in $G L_{n} (Z)$ represen…

math.GR2024

Spherical growth of reciprocal classes in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

Let $r \in Z$ , $r > 2$ , and let $Γ_{2 r} ≅ (Z /2 Z) * (Z /2 r Z)$ be the Hecke group. Let $N_{ℓ}$ denote the set of conjugacy…

math.GR2024

Product of two involutions in quaternionic special linear group

Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity

An element of a group is called reversible if it is conjugate to its own inverse. Reversible elements are closely related to strongly reversible elements, which can be expressed as…

math.GR2024

The Dehn function for Palindromic Sub-Group of $A u t (F_{n})$

Krishnendu Gongopadhyay, Lokenath Kundu

In this paper, we prove that the Dehn function of the palindromic automorphism group $Π A (F_{n})$ is exponential.

math.GR2024

A note on adjoint reality in simple complex Lie algebras

Krishnendu Gongopadhyay, Chandan Maity

Let $G$ be a Lie group with Lie algebra $g$ . In the paper "Reality of unipotent elements in simple Lie groups, Bull. Sci. Math., 185, 2023, 103261" by K. Gongopadhyay and…

math.GR2024

On Dehn functions for family of polycyclic groups

Krishnendu Gongopadhyay, Lokenath Kundu

In this note, we initiate the concept of Dehn functions for a family of finite groups. We investigate the Dehn function for some specific families of finite polycyclic groups. We a…

math.GR2023

Reciprocity in the Hecke Groups

Debattam Das, Krishnendu Gongopadhyay

An element $g$ in a group $G$ is called \emph{reciprocal} if there exists $h \in G$ such that $g^{- 1} = h g h^{- 1}$ . The reciprocal elements are also known as `real elements' or `rever…

math.GR2023

Strongly reversible classes in $SL (n, C)$

Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity

An element of a group is called $strongly reversible$ or $strongly real$ if it can be expressed as a product of two involutions. We provide necessary and sufficie…

math.GR2023

Reversibility and Real Adjoint Orbits of Linear Maps

Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity

We extend classical results on the classification of reversible elements of the group $GL (n, C)$ (and $GL (n, R)$ ) to $\mathrm{GL}(n, \mathbb{H})…

math.GR2022★ 2 cited

Classification and Decomposition of Quaternionic Projective Transformations

Sandipan Dutta, Krishnendu Gongopadhyay, Tejbir Lohan

We consider the projective linear group $PSL (3, H)$ . We have investigated the reversibility problem in this group and use the reversibility to offer an algebraic c…

math.GR2022

Reversibility of Affine Transformations

Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity

An element $g$ in a group $G$ is called reversible if $g$ is conjugate to $g^{- 1}$ in $G$ . An element $g$ in $G$ is strongly reversible if $g$ is conjugate to $g^{- 1}$ by an in…

math.GR2022★ 1 cited

Limit sets of cyclic quaternionic Kleinian groups

Sandipan Dutta, Krishnendu Gongopadhyay, Tejbir Lohan

In this paper, we consider the natural action of $SL (3, H)$ on the quaternionic projective space $P_{H}^{2}$ . Under this action, we investigate l…

math.GR2022

Real adjoint orbits of the unipotent subgroup

Krishnendu Gongopadhyay, Chandan Maity

Let $G$ be a linear Lie group that acts on it's Lie algebra $g$ by the adjoint action: $Ad (g) X = g X g^{- 1}$ . An element $X \in g$ is called $\mathrm{Ad}…

math.GR2022

Real adjoint orbits of special linear groups

Krishnendu Gongopadhyay, Tejbir Lohan, Chandan Maity

Let $G$ be a Lie group with Lie algebra $g$ . An element $X \in g$ is called $Ad_{G}$ -real if $- X = g X g^{- 1}$ for some $g \in G$ . Moreover, if $…

math.GR2021★ 2 cited

Reversibility of Hermitian Isometries

Krishnendu Gongopadhyay, Tejbir Lohan

An element $g$ in a group $G$ is called reversible (or real) if it is conjugate to $g^{- 1}$ in $G$ , i.e., there exists $h$ in $G$ such that $g^{- 1} = h g h^{- 1}$ . The element $g$ is ca…

math.GR2021★ 8 cited

Reality of Unipotent elements in Classical Lie Groups

Krishnendu Gongopadhyay, Chandan Maity

The aim of this paper is to give a classification of real and strongly real unipotent elements in a classical simple Lie group. To do this, we will introduce an infinitesimal versi…

Reversibility and its asymptotic counting in Picard group

On the Product of Coninvolutory Affine Transformations

Classification of Quaternionic Projective Transformations by Equicontinuity Regions

Strongly Doubly Reversible Pairs in Quaternionic Unitary Group of Signature (n,1)

Conjugate reversibility in complex special linear groups

Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups

Kulkarni limit sets for cyclic quaternionic projective groups

On the almost palindromic width of certain free constructions of groups

On the z-classes of Palindromic automorphisms of Free Groups

Spherical growth of reciprocal classes in the Hecke Groups

Product of two involutions in quaternionic special linear group

The Dehn function for Palindromic Sub-Group of Aut(Fn​)

A note on adjoint reality in simple complex Lie algebras

On Dehn functions for family of polycyclic groups

Reciprocity in the Hecke Groups

Strongly reversible classes in SL(n,C)

Reversibility and Real Adjoint Orbits of Linear Maps

Classification and Decomposition of Quaternionic Projective Transformations

Reversibility of Affine Transformations

Limit sets of cyclic quaternionic Kleinian groups

Real adjoint orbits of the unipotent subgroup

Real adjoint orbits of special linear groups

Reversibility of Hermitian Isometries

Reality of Unipotent elements in Classical Lie Groups

Strongly Doubly Reversible Pairs in Quaternionic Unitary Group of Signature $(n, 1)$

On the $z$ -classes of Palindromic automorphisms of Free Groups

The Dehn function for Palindromic Sub-Group of $A u t (F_{n})$

Strongly reversible classes in $SL (n, C)$