S. Rani

activity

20212026

most citedImage of Lie polynomial of degree

2

evaluated on Nilpotent Lie algebra

3 citations · 3 across the 8 of their papers we have counts for

collaborators

8 papers

math.CO2026

Asymmetric Catalan and Shi Hyperplane Arrangements

Sucharita Biswas, Shubhanshu Prasad, Shushma Rani

In this paper, we study the regions of asymmetric extensions of the Catalan and Shi arrangements. We first determine the characteristic polynomials using the finite field method, t…

math.CO2025

Marked multi-colorings and marked chromatic polynomials of hypergraphs and subspace arrangements

Chaithra P, Shushma Rani, R. Venkatesh

We introduce the concepts of marked multi-colorings, marked chromatic polynomials, and marked (multivariate) independence series for hypergraphs. We show that the coefficients of t…

math.RT2025

Graded representations of current Lie superalgebras $sl (1∣2) [t]$

Shushma Rani, Divya Setia

This paper is the study of finite-dimensional graded representations of current lie superalgebras $sl (1∣2) [t]$ . We define the notion of super POPs, a combinatorial tool…

math.RT2024

Filtration of tensor product of local Weyl modules for $sl_{n + 1} [t]$

Divya Setia, Shushma Rani, Tanusree Khandai

In this paper, we consider the tensor product of local Weyl modules for $sl_{n + 1} [t]$ whose highest weights are multiples of the first and $n^{t h}$ fundamental weights.…

math.RA2024

On Commuting automorphisms of nilpotent Lie algebras

Shushma Rani, Niranjan Nehra, Rohit Garg

We investigate the commuting automorphisms of nilpotent Lie algebras $L$ with coclass $\leq 3$ . Our examination exposes the conditions under which the set of commuting automorphism…

math.RT2023

Graded Character Formula for Fusion Products of Irreducible Modules and Littlewood-Richardson Coefficients in Type $A_{2}$

Tanusree Khandai, Shushma Rani

We investigate a specific class of CV modules for $sl_{3}$ and establish an exact sequence for these modules. Utilizing dimension arguments, we demonstrate that this modul…

math.RA2022★ 3 cited

Image of Lie polynomial of degree $2$ evaluated on Nilpotent Lie algebra

Niranjan, Shushma Rani

We delineate the image of multilinear Lie polynomial of degree $2$ evaluated on $L$ where $L$ is a finite-dimensional nilpotent Lie algebra over field $k$ with $dim L^{'} \leq 4$ .

math.CO2021

A study on free roots of Borcherds-Kac-Moody Lie Superalgebras

Shushma Rani, G. Arunkumar

Let $g$ be a Borcherds-Kac-Moody Lie superalgebra (BKM superalgebra in short) with the associated graph $G$ . Any such $g$ is constructed from a free Lie superal…

Asymmetric Catalan and Shi Hyperplane Arrangements

Marked multi-colorings and marked chromatic polynomials of hypergraphs and subspace arrangements

Graded representations of current Lie superalgebras sl(1∣2)[t]

Filtration of tensor product of local Weyl modules for sln+1​[t]